My mini was originally equiped with Cibie headlamps.  Eventually, the glas separated from the reflector so I re-glued the glas and drove for a few years more.  I replaced them in August 2003 with these Quadoptic-Headlight-Headlamp-Kit-Left-Hand-Drive and sent the chrome trim rings to Dimitris in Greece.  Haven't had a problem since.   

Here is another (even more expensive) option. 

//www.jwspeaker.com/products/headlights/model-8700-evolution-2-7-round-par56-led-headlight

Riley,

Local guy has a set on his mini. He seems to like them and they are pretty bright, but they have a strange profile. The stick out quite a bit and are more square. That's the only drawback IMO.

Weird. Have you stuck with the same brand of lamps from the same place? Maybe there's a bad batch. 

Your car might be a good test bed for a pair of LED headlights. //www.truck-lite.com I'm going to get a pair when I wear out my H4 bulbs. 

They must be pretty tough, they put them on these: 

the filament part coming loose inside the sealed unit?

the outside of the sealed unit shows no sign of contact with any body part.

Are they breaking off at the terminal connection on the back or is the filament part coming loose inside the sealed unit? Are you sure that there isn't anything smacking into the rear of the headlamp or maybe the back of the headlight bowl is mashed up against it? Is it happening on both left and right? 

Are you driving like this? //youtu.be/E98K4EZijuw

The wiring harness is brand new with all new wires.  

The bulbs are not just buring out, but they are snapping off where they connect to the plug.  Almost like the bulb is too heavy for the wiring to hold it together inside the bulb.

The light assemblies are sealed units made by Wagner.

I figure if the there was an electrical issue I would simply burn out the bulb, not have it snap off the plug.

Thoughts?  Cheap Wagner light assemblies?

check the wiring, look for signs of premature short circuit like burnt wire, loose connection etc. check the on and off switch as well.  if the wires look old and junky its time to re-wire them. 

open the headlight assembly, you wouldnt believe but at simple as cub webs wrapped around the open wire can cause short circuit and blown bulb.     clean it thoroughly.,  

now while the headlight assembly is unscrewed from the frame, turn it on then slightly and carefully jiggle the wires attached to it and observe and see if it will turn on and off.  it it does then you know the problem is just right there in the wire and connection.

these are the kind of troubleshooting you can't find in Haynes. lol

Something must be loose. Buy a sealed beam unit.

My light bulbs keep snapping/braking inside of the headlight assembly.  I am on my 4th one now.  Headlights were purchased from Napa Auto Parts and work great until the bulb snaps off.

Is this due to how hard the mini hits bumps on the road not working well with standard round headlight assemblies?  Mine I think are H4 standard sealed headlights.

Any suggestions on how to fix?