I recently switched from the LTE RAZR MAXX to the unlocked Galaxy Nexus (Stock 4.1.2) that I bought from the Play store. I am using a Motorola Elite Sliver bluetooth headset that supports both phone calls and audio. I've used this headset with the RAZR, my wife's ATRIX, and several other Android phones with no problems.
With the Galaxy Nexus, if I am not on a phone call, the moment the screen goes into sleep mode, the bluetooth headset disconnects. The headset makes 3 messages in about 15 seconds: "phone 1 disconnected", "phone 1 connected", and "phone 1 disconnected". If I am on a phone call and the display goes into sleep mode, the call will continue. The moment I discontinue the call, I get the same three messages and the bluetooth is disconnected.
The Galaxy Nexus works fine with other bluetooth devices and the bluetooth works with all other phones, but together they have this problem. Any suggestions?