Ah, I see. I did a little digging and did find this
http://www.sandyblogs.com/techlink/2...p-battery.html not for the H2 but may give ya a idea what to look for.
The BUB is a non-rechargeable, lithium battery with a lifespan of approximately 4 years and is designed to maintain an open circuit voltage between 16V and 9V throughout this period. This allows the battery to power the basic functions of the VCIM for least one 200-second (5 minute) phone call at the end of the 4 year span, should a main vehicle battery loss occur.
The BUB voltage is checked every ignition cycle. If the BUB fails the check or if the BUB has had current drawn from it, the OnStar LED next to the control buttons changes from green to red and a DTC is set, either B1446 or B1447.
Service Precaution
Do not disconnect the vehicle battery with the ignition key in the run position.
With the ignition key in the Run position, the OnStar module is awake on the data bus.
The OnStar module is also awake after the ignition key is removed, until Reserve Accessory Power (RAP) times out, or the driver door is opened. If the vehicle battery is disconnected with the OnStar module awake, the OnStar module senses a vehicle power failure, as could occur in a crash, and draws current from the BUB. When the vehicle battery is reconnected, the OnStar LED is red and a DTC is set. Because the BUB has had a current drain and there is no way of telling how long the drain was, the BUB must be replaced.
Refer to Accessories in SI for OnStar battery replacement information.