I think I talked to Wei and John over email and tracked the issue down to the fact that a heartbeat was not being sent from the PC side.
The Mooshimeter will automatically disconnect after about 20 seconds if it does not receive any new commands or requests from the master. This feature is to get around an Android bug where Android would maintain a connection to the Mooshimeter but not share that connection with the app, effectively making the meter unusable until the user rebooted their phone.
The iOS, Android and Python interfaces all ask the meter for its PCB version every 10 seconds as a heartbeat.
Hope this is useful to future readers.