One way to test it is to remove the switch and hot-wire the car.  If it doesn't die, the switch is your problem.

They could both be related. Replacing the ignition switch would be a good place to start.

dies like it was turned off. I also have a symptom with the ignition key that must be related. IE: the start function of the key does not always work. You have to turn it back and forth a few times . The ignition light turns on fine, but the next position of start does not. I am now thinking the contacts in that replacement ignition switch may be the issue. I can't find any loose or worn wires anywhere else.

Jerry

Very odd sounding symtom this, Does it just die like it was turned off? or slowly peters out?

You can snug up the tab on the temp sender by gently tapping on the rivet with a small punch and small hammer. 
Plugs and firing sound OK, as does fuel supply.
You need to check the complete low tension (12v) circuit that feeds the coil - from the supply at the solenoid or hot side of the fuse box to the ignition switch to the coil, and then the coil ground. It could be a loose connector somewhere that 'shakes and breaks' when the engine is at idle. It may also be 'skipping' when rpms are up but isn't noticeable because the engine is turning fast enough to hide it and keeps running. Check your engine ground strap too.

Pumped fuel from the electric pump into a big jar. Consistent pumping, filled over a quart and no bubbles, or stopping. Timing light on the plug wires showed all are firing. Plugs look perfect in color, the tips where the plug wires connect were bent for some reason. I am going to buy some new ones anyway. I checked for loose or rubbing wires. NOTE to those using stainless steel braided hoses for the oil cooler, any wire touching the braided stainless gets abrasion. Nothing worn through but some were abraided. I unplugged the temp gauge sender because the connector tab rotates around, might replace that.

More checking to come.

Jerry

I hope you had a good sleep.... when you were supposedly reading what I wrote. But you are WRONG AGAIN. You had the sequence of vacuum events all wrong as it affects the dashpot.
Just go back to sleep.
For the record, I did not agree with anything Tony wrote.
.

Good that sir Dan FINALLY agrees with me.....i can now have a good night sleep tonight.... haaaaaay!!!!

Dual SU 1.5 inch, and they are new with the rebuild, maybe have 3000 miles on them. The hoses are good, I just checked them. So I will start on the other suggestions. And after your definitions, the car has a stumble!

Jerry

You should take some reading lessons.

You believe wrong...  2½ - 3 psi is all you need and SU's are very sensitive to higher pressures.  Fuel flow rate is far more important than fuel pressure. 

Jerry:
Which carb are you using, obviously an SU with  a dashpot?
I am thinking fuel delivery somehow> Did you replace the rubber lines when you built this up a short time ago.
And I guess if it is an HIF there is no easy way to check the float bowl.

A couple of terms to clarify:
- a "miss" is when one or more cylinders intermittently fail to fire properly. causing the engine to run rough, though it does keep running.
- a "stumble" is when it loses power momentarily but usually keeps running and catches up. Like when you trip on a crack in the sidewalk but don't fall down.
- "hesitation" is a lesser stumble - a delay in power increase.
- a "stall" is when the engine fails to keep running and you need to crank it again.

A miss usually results from poor tuning - timing, mixture, bad plugs/wires etc.
A stumble usually results from tuning problems or the 'accelerator pump' effect not working because you forgot the dashpot oil.
A stall occurs when for one reason or another the engine does not produce enough power to continue running. This could be loss of spark, loss of or too much fuel, or too much load for the available air/fuel mixture, like when you let the clutch pedal out without pushing the accellerator pedal.

On SU carbs, pumping the gas pedal does absolutely nothing but open and close the throttle.

On the assumption your carb linkage including choke are correctly set up, pulling the choke out about half-way (a little less actually) should richen the mixture as you were trying to do. After a certain point - about 1/3 - the choke mechanism should be engaging the throttle mechanism to increase rpms to assist in warm-up. So pulling the choke out as you did would have modified a fueling problem.

One area we haven't explored is the possibility of an air leak. Check to see that all the carb and manifold bolts are tightened to spec. Then, if you can keep it running long enough, use a rubber hose like a stethoscope to listen around each gasket area and hose connection for the hiss of air being sucked in where it shouldn't be. Or, if you have an unlit propane torch or can of ether, you 'leak' this fuel around the gaskets etc. and listen for the rpms to increase.

Electrically, check the low voltage connections to the coil and the 123 ignition system. If you have a tach installed, try disconnecting it. I don't think the electric fan plugged into the cigar lighter is an accurate assessment of electrical condition - it is a constant load and its speed changes would not be apparent (unless you have stroboscopic eyes!). The ignition system draws comparatively very low current. Your fuses should not matter because the ignition system is supposed to be unfused. Depending on what you have added as accessories (like the fan and cig lighter) you may be taxing the electrical system. If your car is a 1968, it probably came with a generator and voltage regulator. This system is intended to provide enough regeneration to keep the basics like the original lights, wipers and heater fan working... barely if all on a t once. If you still have them in place and you've upgraded your headlights, added a stereo and your electric fan, you'd be overloading it. The generator can't keep up and maybe the voltage regulator takes a hissy fit. If it has been converted to an alternator, then it might be more complex. [Having it cut out suddenly when rpms drop below a certain point suggests a charging/voltage regulation issue to me. Generators generally lag below about 1000 rpm.]

The only other thing I can think of is that you riled Lucas, Prince of Darkness by having a cigar lighter in a car that was designed without one.  Bad "carma".

What I thought your post was about.....

don't rule out electricals yet,,have you pulled the plugs and inspect the plug wires for damage? if you have a timing gun you can test the plug wires if it's giving intemettent current, hook the timing gun to each of the wire one after the other and see if it's flashing in a timely manner, the strobe light should not miss flashing, if it does then you're getting a gadam misfire. address the issue./

On the fuel system issue: pull the line that lead from the fuel pump, insert it inside a clean empty glass bottle, crank the engine ,see if fuel comes out of the line, if yes then your manual fuel pump is ok.,there is a standard fuel pump pressure as well. i believe it's 2.5 to 3psi., if it's low, address the issue as well. Be careful in dealing with the gas, and gas tank...don't be like the Binky's, sawing the mouth of the gas tank with a metal saw...oh gawd!!!

if you really want it to idle good....just adjust the idle screw..problem solved!!!

idle screw is the most neglected part of the mini,,, besides the ashtray..

Feedback on the dampers. oil dripping from the pistons, but it was not full. Topped it up and took it for a drive. Still shuts down at times. It is almost like the fuel pump stops. I have a back up pump, and my try a replacement. Another test run: I pulled the choke out halfway to see if that made a difference. Nope, still stumbles. When it stumbled, I pumped the throttle to see if there was any effect, none. I watched the electrical fan plugged into my cig lighter as the car stumbled, no change in speed, so it was not an overall electrical fault. My new electrical tester will be here in 3 days so I can test the power to the distributor.

thanks

Jerry

Once you get that detailed (though simplified) explanation under your belt, then you can see how different weights of dashpot oil can affect the transition from closed to open throttle. A heavier oil increases the accelerator pump effect and a thinner oil decreases it. Which seems counter-intuitive. (I'm sure Tony, with his double psych major, can see that.)

To correct where mini4ever is wrong again: 
There is manifold vacuum created by the cylinders, and it is highest when the throttle is closed. But the small port in the SU carb which operates the dashpot is before the throttle. It does not work on manifold vacuum at all. It works on vacuum resulting from air rushing through the carb when the throttle is open. The wider the throttle, the faster the air flow and the more vacuum is applied to the dashpot. Now, the dashpot does 2 things. The bottom end of the dashpot piston forms half of the venturi - the part of the carb throat that causes a reduction in air pressure that draws fuel up out. of the main jet and helps atomize it. That's the first part. The second part is that the main jet needle is attached to the bottom of the dashpot and gets pulled out, allowing more fuel to flow in direct proportion to the air passing through the venturi.
At any particular throttle setting, the dashpot is metering fuel and air at the same time in appropriate proportion.
But when you put your right foot down suddenly on the accellerator pedal, opening the throttle suddenly, you mess up this balanced system by suddenly allowing more manifold vacuum to suck on the carb. The dashpot suddenly wants to open more. This makes the venturi momentarily too wide, reducing the draw on the main jet and the fuel supply lags. The result is a stumble or hesitation. But the smart guys who developed the SU carb solved this by adding the dashpot damper to slow the reaction of the dashpot to CHANGES in throttle.
Now what happens is when you stomp, the throttle opens, the vacuum is applied to the carb throat with the venturi still mostly closed and the main needle still way down at the idle setting. You'd think there wouldn't be enough fuel to accelerate, but the vacuum can't get enough air, so it sucks much harder on the main jet and EXTRA fuel gets pulled instead. This is the 'accelerator pump' effect. Fixed venturi carbs like Holleys have and need an accelerator pump to compensate for momentary leanness when the throttle opens. (In fuel injection the computer uses the throttle position sensor to do the same job.)

What utter bollox's Tony, you really should just shut up........................

YES, there's a possible flooding.  here's some things the "expert" do not know.   We should remember that there is still vacuum pressure at idle(1000rpm). it's  the vacuum pressure which makes the carb piston goes up. and is regulated by the oil inside the dashpot. NOW, since there is pressure at idle, the tiny pressure created at idle makes the piston goes up abruptly since there is no oil inside, then gas will flow....AND since the butterfly inside the carb does not open because you didn't step on the gas pedal(idle that is), there is now LESS flow of air.   You may have noticed,when you start to step on the gas pedal, it started to ran fine, it's because the venturi opens up,allowing more air to come in, enabling the gas to burn better.


Concluding remarks:: More gas that goes inside the engine with less Air...this creates flooding. ,,(me and mystacreation were right).



"someone" else is wrong...





SO, bottomline----->  check the dashpot oil level, period!!!!






common sense is not learnt in school...it's comes out naturally  !!!!

I will check the dashpots tomorrow. Answers to #1 The car starts well, idles well, runs for 4-5 min, then it is just like the electric is shut off, it stops. Starts right back up immediately. If you use the choke, the idle increases, (no surprise) , but it still stops. answers to #2 Easy to start, without choke or pushing on the gas pedal. Fuel needles prior to this issue seemed about perfect , the plugs were the right color. I will pull the plugs out tomorrow.

Excellent matrix to check the issues. Thanks very much for the suggestions.