The mooshimeter updated its firmware to version 1446183524 (UNIX timestamp for Oct 30th).
This has not helped the connectivity issues on AC at all.
I am testing with V and common connected to US 120v 60Hz mains, and the other jacks left open.
I have noticed that if I leave channel 1 on temperature, and channel 2 in AC voltage (auto, 4000Hz/256 smpl) the meter can stay connected for up to several minutes before disconnecting. After sitting connected for a couple of minutes, if I switch modes on channel 1 from temperature to 'Current DC' by tapping the 'INT' , the meter disconnects in 3-10 seconds with 100% reproducibility.
The hardware is nice, but the firmware/software on this device leaves quite a bit to be desired...
Edit: I was able to remain connected for over 30 minutes in channel 2 diode test mode, by leaving channel 1 set to 'Current DC'. I then toggled channel 1 to 'current AC' mode and was disconnected within a few seconds. This is another 100% reproducible method of achieving BT disconnection on my hardware/software configuration (iPhone 5S, iOS 9.1, v1.06 app).