My '04 Cooper S was doing this recently after the switch to the 10% ethanol fuels. It was stalling after the first start or needing extra cranking time to get started, and occasionally would stumble/get rough at idle after running on the highway (like at an off ramp). The car was in to MINI Peabody over the past weekend for a wheel bearing replacement, and they reflashed the DME and the problems have gone away.
My MA, who took the car in for its appointment, mentioned that a lot of owners are having this trouble lately due to the fuel switch.
I hope it's a permanent fix for you, but the problem is that whenever they re-flash, all the learned stuff is erased and often, as the car re-learns, the issues all come back again
Or ... the car now learns to work on summer fuel, and then the issue recurs when we switch back to the winter formulation in late October / November
Ian C. Gloucester, MA, USA (UK expat) driving GPMINI or a non-MINI!
yeah.. I dunno, I think it's more than a software thing like Ian's thinkin'...
Still crappy starts for me today, but runs great.. took it ou on the highway and opened her up.. she's doing much better with the lower octane.. (so what do I do?.. I was looking for some upholstery cleaner that Pete had at the local PepBoys.. yeahhhhh.. I bought a can of this fuel stuff that has NitroMethane in it.. YEEE HAAAAAWWW!!... probably not too good for the motor.. and it's NOT street legal.. but it works.. )
definately the same probs for me, '04 MCS/JCW....starts and dies, idle revs are low. Sometimes the trick of turning the key on to pos 2, waiting a few secs and then starting help.
I've been running Mobil 91, Sunoco 91 and Citgo 91, next tank I'm going to try 87. Then again, I'm going to MoP on Monday to get my new tires mounted, and I won't fill up by then....I'll ask there as well.
I filled up yesterday - VPower - but we still have the old blend and no ethanol yet so no problem here. I'll post back when they finally change it in Maine.
In Canada, I quite often use Mohawk or Husky mid-grade (E-10 94 Octane). I have not had any problems with cold start. In fact, my gas mileage appears to be up a bit over non-E10 91 Octane gas.
However, there is the possibility that I have a slight decrease in low-end torque as I noticed I chirp my tires more from a standing start when not using the E-10 stuff .
05MCS BEP
Alta 22mm rear anti-swaybar, Madness CAI, Alta 15%, NGK BRK7EIX, M7 Strut Tower Reinforcement plates
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...although, all kidding aside, they may have it further south. 
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05MCS BEP 
