Thanks for the quick replies. I unfortunately don't have another phone to pair it with. Don't know the part number, but it's gray and black with a blue light. It has previously worked with this phone (a Verizon phone) for over a year, but the problem started just recently. I did, however, update the phone's firmware about a month ago...
In any event, pulling the battery on the phone, rebooting it, and then re-pairing it with the bluetooth module again seems to have solved the issue. This seems to confirm, as grantwoodtx indicated, that the issue is related to the firmware upgrade.