I had a similar problem but after getting good advice from 3hummers and others I ordered a PMD (pump mounted driver). Mine had been located close to the engine and when it got hot it stopped fuel from getting to the engine and the 97 H1 cut off. After it cooled down, I could restart it but after heating up it stopped again.
After I took the old one off and mounted the new PMD on the firewall away from the engine I had no further problem.
Now I have a CTIS front tire problem that I need to make a new post to get help with :-(

 

Had the same issue! It ended up being my fuel pump that went bad

 

Now my cruise control went out,,,,fuse is good,,not sure what else to check

 

Installed remote PMD on 96 TD,,runs great ,no more trouble...very easy job to do ..I left the old on pump...thanx for help from everybody on here...

 

"Installed remote PMD on 96 TD,,runs great ,no more trouble...very easy job to do ..I left the old on pump...thanx for help from everybody on here..."

Hey cobra what did you find on your cruise control?? Curious cause I currently have the same problem, fuse is good. Thanks!

 

I havent beat that problem yet.....just went out a few months ago

 

A PMD is an electronic switch that controls the fuel flow on a Stanadyne DS-4 electronic injection pump. Electronic injection pumps are used on all Hummers with the GM 6.5 turbo diesel between 1996 and 2004. When a Fuel Solenoid Driver fails it will not display an engine light.