Thanks for the update!

Wouldn't have guessed that.  Glad the issue was fixed.

Ken

UPDATE: The in cabin fuse box went bad. Shop replaced the whole things and everything now works. 

It sounds like you have the 'half full' engine icon and you still have full power (not in limp mode) and no error codes...

From what we have seen, a couple items stand out more than others that may be causing this:

Loose gas cap
Faulty Thermostat Housing (sensors)

Other problems have caused this light but not as frequently as the two above.  The other causes are all over the map including high pressure fuel pump, vanos sensors, vacuum leaks, etc etc....

Some have reported an Italian tune-up cleared the light (a couple of full throttle runs to redline)..

Best to have a BMW/MINI specialist take a look.

Ken

When you say the engine dies, does it drop to idle, stumble or completely shut of, requiring restart?
I'm not familiar with your car - does it have a separate "engine light" as you call it and this engine icon in the tachometer (rpm display)? I am guessing this 'half-full engine icon" may mean your engine is not performing optimally and it running a reduced power.
I doubt it would be a problem directly with a catalytic converter - that would probably show up as problems during high speeds, not during decelleration.

Is the engine half full or half empty?  

Computer shows no fault codes. 

That engine icon is definitely half full. Sorry, there should be a code to read.

Im having some engine issues with my 2010 Mini Cooper Clubman. The engine dies when coming down from high speeds. Im guessing its the catalytic converter, but my engine light isnt illuminated, but I am receiving a Engine icon on my RPM display (see picture). The manual doesnt tell anything about an Enigne Icon that is half filled in and half not, like the one in the picture. Im also having issues with my power windows while the engine is off. 

Does anyone have Insight on this subject, before I take it into the shop? 
Thanks.