ok - nm. I used my Innova and tested battery on 12V; running and not running.
Not running --> averaged @ 12.71
Running with lights and radio on --> 14.35 - 14.40

 

I'm going to suggest finding a place that knows there stuff and paying to have this problem tracked down. I very seldom go this route but this is one time it could pay. DO NOT take it to a dealership!
Find a place that specializes in electrical issues with cars. Or you could just start replacing stuff.

 

Your battery is fine. When I say consistent, I mean that you have solid ground and positive connections (ie. your new battery terminals are correctly installed) and that the PCM is correctly plugged in.

Take a good look at the connections to the PCM and check that the gray lock latches are down all the way like in this pic. If you never messed with the PCM, it should be fine, but are you the first owner?

 

Update - cleaned throttle body and throttle body sensor. Problem still exists. Ran and idled better though, but problem still there. Will try NEW señsor next. Battery is fine. PCM has all connections ok.

 

I had the same issue. It was the throttle body. I kept cleaning it every 6 months and it fixed the issue. Just last year I got a card in the mail saying it was a recall and they replaced it all and haven't had issues since.

 

Reduced power , service stability , stability failed , all most probably related to bad throttle body . Just have to change it .. Just changed mine today , all well again ..
But check the obvious first , like no leak anywhere from rubber intakes on the TB itself .
That would also cause bad idling and engine dying sometimes ..

 

I stand by my earlier post: "Highly unlikely a P0601 has anything to do with the TB." Consider this thread is about a P0601 CEL, not rough idling, little more specific than that.

 

Reduced power Sys Stability warning on my H3 months ago. Cleaned throttle body and Mass Airflow sensor with cleaners from Walmart and problem stopped. Then for the past two weeks unsteady idle cropped up but with no Sys Stability warning. It was found to be the MAP sensor which was replaced. Running fine again.

 

Update - PROBLEM SOLVED. Issue has been corrected by new PCM installation. Installed a few weeks ago and has been ok since. Thanks to Hummer Forums for being the one to help and solve. Dealer was of no help at all!

 

During my eight years of ownership i've had to change 4 throttle bodies , all used ones .
They work for a while . I found that it takes time for the ECU to adapt to the different TB
something like a month with bad idling , then once it learned , all is well again .
Is there a new , updated TB on these that could last a while ?