Have you tried to reset the bluetooth adapter with BluetoothAdmin? I've added this feature to B4A-Bridge and it sometimes solves similar issues.
Thank you for that suggestion. I had hoped that would help, it may help but it is not a reliable solution. Here are my observations so far.
The usual sequence is power up Tablet, power up the BT module then run the app.
Connection success or failure appears random with perhaps a bias towards success. If connection succeeds the app can be started and stopped multiple times and it will always connect.
If the connection fails it will probably also fail if another app like BlueTerm is tried. Restarting the app generally, but not always, still gives a fail to connect.
In this state however a PC can connect to the module without a problem.
Turning Bluetooth off then on again in the settings system screen then re-running the app usually still results in failure to connect.
I have tried a modified version of the program where BluetoothAdmin first disables Bluetooth then enables it (following the full turning off, turned off, turning on, turned on flow) but the connection still usually fails.
BluetootAdmin discovery always finds the module.
The only guaranteed way I seem to be able to connect is to manually un-pair the module then pair it again. Connection, so far, always succeeds after that.
I guess the next step is to try to un-pair and re-pair in the program.
For those that are interested I will report back. As usual any thoughts or suggestions welcomed.