I have an '07 GT with a stalling problem too. Normally happens when coming to a stop - more likely to happen when stopping in a hurry. From what I have read this seems to be a fairly common problem on all models of K bike and I can't see that there is a common solution.
Mine started stalling after a new airbox was installed to cure the BBS (jerky throttle) issue. I only got the airbox, not the software update that I think is supposed to be done with it.
Since then it's been back to the dealer twice for the stalling thing. First time for 10 days (dealer couldnt reproduce the problem....then it stalled on the way home when I picked it up!)
2nd time it was in for a month, after I demonstrated the symptoms in the dealer forecourt. Try this yourself - while stopped, try to hold the rpm's steady at 2000 for a while, then let go the throttle. The revs on mine dipped below 1000 and sometimes didn't recover to idle.
That time it got a new fuel pump controller and EWS antenna ring on the advice of BMW N.A.
Well that still ain't fixed it, as it stalled on me yesterday. I have to say though, it's better than it was. Prior to going in to the dealer the 2nd time it stalled 10 times in a 25 mile commute. In the rain. In heavy traffic.
I've a feeling that the software upgrade would help, but the dealer don't want to do it because (he says) there is an issue with the latest upgrade which locks up bikes. Yeah, right
Worst of it is, I have an '05 K12S which has started the same shennanigans. I'm rapidly loosing faith in BMW bikes.