sim800 will only work while usb plugged into PC

I use Nano and Mini Pro on SMS emergency call system.

I have tried genuine Arduino Nano and Mini Pro as well as Chinese clones.

My sketch works standalone with cheapest m590 module using Nano and Mini Pro, no problem.

AT commands are the same on M590 and sim800 for the features that I use.

When I use sim800, it works on the Nano as long as my usb cable is plugged into PC. Still no problem.

but.....

When I remove usb cable from PC it will not work.

It does not work on Mini Pro at all.

The module remains connected to the network, which I establish by calling the number from my cell.

I have tried sim 800DS, sim800L and smallest sim800l modules. They all do the same.
I have tried plugging the usb into PC with all programs closed - still works
I have tried plugging the usb into 5v usb supply, does not work.
I have tried connecting to different power supplies.
I have tried adjusting voltage from 3.5 to 5v with 10A variable bench supply.

Like any good technician with dirty fingernails, I have tried giving it a good bang and swearing.

I can hear comms with the network through random noise through my PC speakers and there is no attempt by the sim800 to communicate when usb unplugged, but of course I am working blind as I cannot follow what's happening on serial monitor when unplugged.

I realise I am missing something and I will probably feel a proper fool when it gets pointed out to me.

I am ready to give up and use only M590 module, which is a pity because any future enhancements like voice etc. is then off the table and I will be stuck with a shoebox full of sim800's.