Hi,
That's totally normal, bike switches fuel pump and everything on and then is on standby mode. If you push the starter button then everything comes alive again
Or if you even gently push the kickstarter, then the pump should start again for few seconds....if not then there could be problem with ECU connector or pick-up coil.
In GuzziDiag check if the program sees the cable:
Go: File - Preferences and then is it showing COM port? (should show "Port 7" or different).
Do you have correct motorcycle chosen from there also. I usually choose Breva 750, it uses the same ECU as GasGas.
Just in case, what year is your FSE?