Have you checked for wear on the master cylinder clevis pin ? Any wear on any of the pivots multiplies itself by the time you get to the slave cylinder. I seen a Moke once without a pin and tons of play with hardly any clutch arm movement.

I noticed today with help from a friend that when the clutch pedal is pressed the clevis pin is tight and the plunger into the master cylinder starts moving immediately.  However, when he watched the clutch arm while I was pressing the pedal, it did not start moving until I had about 3/4" to 1" of pedal pressed.   

How much travel should the arm move with full clutch pedal?   It doesn't look like very much, and somewhere between the master cylinder and the arm, there is about 3/4" of lost movement, which appears to be inside one of the cylinders (main or slave).   

The he main and slave are new and have been bled several times.   Almost sounds like one of the seals has flipped inside the cylinder bore.    

Craig

My primary gear is the original style and gear, and I reused it as it was still in good shape, so it has now seen tens of thousands of miles trouble free.  That seems an unlikely culprit.  I'm hoping it may be a sticking plunger or something mechanical of the sort.   

This is probably more likely when using the Minispares slip-in floating bush. It is silicon bronze, non-porous, and maybe doesn't like running dry.
It's very thin wall, and it's important that it's not defomed out of round. This can happen when trimming & fitting it (often they are a little bit long).
I have one in my 1360; have had no problems, but I suspect it does drag slightly when hot. But hardly noticeable.

You can pull the flywheel in the car and have a good look. A binding primary gear bushing can also cause grief. 

For the first year or so after the rebuilt transmission this problem did not exist.  It didn't even exist for the first 6-months after the new master cylinder, slave cylinder and braided stainless hose were installed.  It has just started to appear over the past few drives.  I still need to check for the same clutch arm throw when hot as it is cold, and change the oil.  It doesn't seem likely to be a tight idler gear just appearing after a year, and another thing not mentioned previously is that the clutch was replaced during the same rebuild.     

I had this problem? on a Mini years ago. Turned out the idler gear was tight, had only .002" endfloat. Was OK cold. When things warmed up it started to bind in the case, then the synchros couldn't synchronise gear speeds so it wouldn't shift properly.

Changed an idler thrust washer and all was well.

I had a similar problem in a Dodge Caravan with a 2/5L Turboand the Getrag 5-speed manual tansmission, but it was cold-related, getting clutch "drag" when the engine was cold. Near as I could figure, the tolerance of the clutch/shaft splines was too close causing it to bind when cold. The clutch wouldn't slide clear of the flywheel and dragged a bit until warmed up.

Maybe in your case, the primary gear is expanding with heat and is either binding in the splines or it doesn't have enough end float clearance and is clamping down between the primary thrust washer and the retaining ring. Or maybe just too tight on the crankshaft. (Guesses!)

Not a Mini but i have an intermittent similar problem when warm with an old Mazda truck with a hydraulic clutch i keep around for hauling. Sometimes when trying to get it into 1st gear it does not want to engage and to get it to engage i need to try another gear slightly (not fully engaging) usually 3rd or 5th works best ??? and then it drops into 1st fine, it also works fine if i shut off the engine. I have since checked it out more and when trying to overcome the resistance in 1st it tries to creep forward as if the clutch is not disengaging fully. I drove it about a month ago and the clutch felt different and started slipping and i figured oh well its time for a new one. The next time i got in it the clutch was fine no slipping so i think my problem is the clutch is hanging up/ binding on the mainshaft or the slave is not working fully but that is located inside the bell housing !!!! Mini's that have this problem occur usually have it when cold not hot.

My ideas are eliminated, then. Check the 'throw' of the clutch lever hot and cold. You can do it yourself by holding down the clutch pedal with a stick, although I do not think its the problem.

Synchro rings were replaced with new two years ago when I rebuilt the transmission.  I'm using Valvoline VR1 20W50.  I will try changing the oil to see if this makes a difference.  Oil is about a year old, but has less than 4000 miles on it.  thanks!

If the clutch arm moves the same amount away from the stop bolt hot and cold then it is not a hydraulic problem. Not going into 1st very well when the oil is warm suggests a worn out synchro ring wherein the ridges are worn off and can't 'grip' the synchro cone. Are you using synthetic oil? I have heard from a respected local Mini mechanic that synthetic is too slippery. I don't remember what happens going into reverse but synchros are not involed, so maybe a separate coincidental issue. 

My clutch began becoming difficult to engage first and reverse recently.  It is a 4-synchro box with Cooper S gears bolted to an S motor and remote change.

6-months ago my clutch stopped working (no movement of the arm when pressing the clutch pedal).  It was obviously a hydraulic issue, so I replaced the master cylinder and slave cylinder with new. I never found out which one was the problem, but the master cylinder had been rebuild once already and the slave looked original.  I also replaced the hose with stainless braided and switched to DOT 5 silicone fluid so it would be the same as my brake fluid. 

When the car is cold, the clutch works fine.  Once it warms up, it won’t engage easily if at all.  I have bled it multiple times, no air comes out, and this makes no difference.  I backed out the 15/16” stop nuts so they are ½ rotation from touching the cover when the clutch pedal is pressed.  I pushed on the arm with the spring removed and moved the arm stop bolt out to touch the arm and then backed it in ¼ turn.  The linkage, clutch arm and plunger were all inspected 2000 miles ago when the car was apart, and they are in good shape.

What throws me off is the temperature thing.  When I let it cool down, the clutch works fine again.   Normally, this would point me toward the hose swelling from the heat, but as it is a new stainless braided hose, this doesn’t seem probable.   Maybe replace the hose and see if the problem goes away, or could it be some other hydraulic (or mechanical) issue that is affected by temperature?  

Edit:  I also checked my crank for movement, and there is none.  The engine RPM does not change either when pressing the clutch.

Thanks