This is a pretty odd problem but normally the keyless entry disables based off of the key buzzer or the ignition being in "ACC" or "ON". VW's I'm not sure which off the top of my head it is (buzzer or being in "ON") but I do know normal operation when in the ON position means the keyless entry is disabled.
This would lead me to believe there is some type ...
The flap lock mechanism is at least in my Polo a simple pneumatic pump.
Remove the side of the trunk liner behind the fuel flap.
It should be an pneumatic pump there with an air hose to the lock (the lock is a pin which is driven thru a wedge on the flap's inside.)