The first thing I would check :everything to do with fuel, such as sensors, gaskets, filters ,lines, injectors, rails etc..
I know its very broad but so is your problem. As some of the other members said this is a some what common problem, but everyone has had a different solution. I would start general and move into the specifics.
Something is not flowing right, and my guess would be involving A/FR. Just because your gauge or AP says you might be running the proper a/fr doesn't mean its 100% accurate. A O2 sensor could be loose throwing it off etc.. Also another common reason for engine cut or fuel cut is over boosting, check your waste-gate duty cycle.
*please note that this doesn't mean i'm right, its just what I would do, hope this helps.*