I’ve also noticed my own phone/mooshimeter combo appearing to get stuck in firmware update mode, but I was always able to un-jam it by quitting the app (swipe it out of the phone’s app list) and putting the phone in aeroplane mode for a few minutes. Once I rebooted my phone, but I’m not totally sure it was necessary in order to reset the connection.
James has mentioned that Android’s bluetooth system is a bit of a mess. If it’s half as bad as Linux bluetooth, then it’s an absolute nightmare to work with. Other manufacturers deal with this by simplifying the wireless communication: not allowing firmware updates, requiring configuration buttons on the remote device, not having low-power standby modes, not having multiple data channels, etc. So really we’re lucky that somebody is trying to make something better out of a very complex and difficult technology.