Hello Steareth-4
I don't even have the thing in use anymore, but have reactivated it now anyway, oh what am I nice again! :-)
Test: Connect mobile phone and pair via BT. I disconnected the Logitech adapter from the power supply for 5 minutes, plugged it back in, and the phone connected again straight away. I am confident that it will work for longer than 5 minutes.
Greetings, mikeych76

It should, yes. But the mobile phone should do the rebinding, not the other way round.