2001 Suburban 41000 8.1L 2500 series Engine quits

Hi I just got my suburban in may with 37000 miles. About a month after I had it, I was about 3 miles from home and the engine just died. I pulled over to the edge and after a couple of minutes, it fired right up. In the last month and 1/2 it has quit about 5 more times. Always randam. Always while I'm driving. It's like I have cut the switch off. After it sits for a couple of minutes, it fires up and purrs like a kitten. Yesterday, it quit close to the advance car place and I had the battery and alternator checked. This morning it quit 2 times before I could get to work, only about 6 miles. I'm worried I'm going to get run over in the middle of the road.
I would appreciate any suggestions to the problem
Thanks
Lisa