check to see that whoever installed your unit with the gm Lan adaptor (probably a GM -oso1 or oso4) used a relay on the switched output.
the lan adaptor might need a relay to be triggered, instead of connecting to the 12 ign wire.
im am more willing to bet that they wrong adaptor is being used. and its NOT the onstar adaptor.
The adaptor shoudl interrupt FRONT SPEAKERS only when onstar is activated. The problem you are describing is that whoever installed it is interrupting power to the radio.
The only logical explanation for this is, that the shop/installer didn thave to correct adaptor, and somehow needed to stop the radio from comming out the speaker at the same time as the onstar. so instead of using the correct adaptor, they used a relay to shut off the radio only when onstar is active.
OR
you have a bose system, and you cant actually turn off the factory amp when onstar is active because then you wont hear the onstar, so they just shut off the radio.
in either case, it seems like the wrong Lan adaptor was used. There are 7-10 different GM lan systems and adaptor.
go so Metra's website and see which is the correct for your vehicle.
you will need to know the following
Year
Make Model
Onstar (yes or no)
Bose (yes or no)
RSE (rear seat entertainment) (yes or no)
Factory nav (yes or no)
good luck
Wolfz23