I have 2006 H2, 95k mi. Lately we have been driving our other vehicle, an H3, it's in a kind of drive it until it dies state. I hadn't kept up on running the H2 to keep up the battery charge and it died a couple of weeks ago. Got it jumped, had to do this again last night by AAA, drove it for at least an hour, most of which was freeway driving, but now it doesn't hold a charge. Battery is dead. Is this just the battery or is there something keeping it from charging when driving?

 

Do a free battery load drop test at you place that sells batteries. If good, do a paid AVR test. Simple.

 

The alternator charges the battery. The battery just basically starts the engine and runs all the electrical when the engine is NOT running.

So if your battery is not holding a charge, it's either a worn out battery or your alternator is not properly charging the battery when running, which means it could be both. Btw, if it is a bad alternator altogether, your H2 would not run long.

Start with a battery check, if its good when charged, its the alternator.

 

Battery SOC (state of charge) and battery SOH (state of heath), a battery can have a good SOC but a bad SOH, imagine putting 8 x AAA batteries in series, they'll measure 12V but can't start a Hummer. This is why a multimeter can show 2.8V but doesn't mean a battery is good.

Conversely a battery can have a low SOC but a good SOH, it just needs charging.

Allowing a lead-acid battery to run down for long periods (below 11.5V) can severely affect it's it's SOH health permanently.

Parasitic "drain" or "draw" ("vampire drain") is down-side of battery systems, it is hard to measure and according to GM bulletin #02-06-03-010A for a Hummer should be around 30mA (0.030A)
A 30mA draw will drop SOC from 80% to 50% within 30 days and 75mA within 11 days (non linear relationship)

Eg I had a plug-in TPMS (tire pressure) which put the draw over 90mA and killed my battery within a week, so check nothing is adding to the draw e.g. aftermarket equipment such a alarm systems, GPS tracking or anything plugged in to the 12V accessory points.

Get a battery tester or load tester, something like a TOPDON BT100, these are really special bits of kit that do an amazing job taking all the guess-work out of battery diagnosis. These are more than just a voltmeter and use complex AC, DC and load measurements to determine "internal resistance" a measure of a battery's SOH.
FYI

 

Knowhum did you ever find out your problem? I just tried to start my 08' & it seems like the battery was dead but I couldn't even take my key out of the ignition or even take the vehicle out of park? Anybody ever had this problem, I put a trickle charger on it but that didn't help, I had to go out of town but when I come back me & my son in law are going to try & find out what the issue is but I thought I would ask & see if anybody else has ever had this problem, thanks

 

It WAS the Battery! GL with your issue if you haven't solved it yet!