I had this issue on another vehicle, turned out to be a loose battery cable. Somewhere along the way the battery cables were replaced and were slightly larger at the connection to the battery post. They appeared to be fully tightened yet had just enough movement that caused the engine to die intermittently.

I would also double check the Crank Sensor, no loose or cut wires at the harness?

I replaced the crank sensor already and it shut off the next day

Well replaced the ignition switch on Saturday and ran fine on Sunday. Wife took it to work on Monday and it died twice. getting rid of this thing as soon as possible...

Update
 

So my local dealer told me to call GM customer service and start a ticket on my hummer, called and the person I talked to said they would help me anyway they can, they are going to call my dealer and get the paperwork from them about the hummer shutting off, she told me that it is a safety issue, I have my doubts that they are going to help me, stay tuned....

I'm thinking some electrical connector has a pin backing out or maybe the ECU has a bad solder joint on it?

Thank you sir, I will look into it

2004 H2 intermittently dies
 

Hi,
Your story sounds very similar to mine. Did you replace the ignition switch? Did it solve your problem? Or was it something else?

I just read all the posts. Any updates or did you get rid of the Hummer?

Same problem H2 coughs and dies while running
 

Looks like not ignition switch but maybe loose battery cables or alternator...starts up again immediately upon dying but will die when accelerator depressed rapidly or very far, so it is a bit of a safety issue.

I actually just posted yesterday the same thing with my 06. Same exact thing. And replaced the ignition switch also.
Was there any outcome? Intresting part with min is that my issues happen only when the main feed for the fuse panels are connected to the batter. Now threw the auto start battery saver thing