I'm not sure quite how those work but it might be worth tracking down the oil pressure sensor and giving the connections a good clean (both on the sensor and the connector block spade fittings).
I'm guessing that the quick startup doesn't give the sensor time to send back a reading, which might be causing the error message, whereas performing the check might give the "brains" a few goes at getting a response back from the sender.
It doesn't sound like you have genuine low oil pressure if waiting a few seconds before starting the car prevents the error... but check the oil anyway. Fill it to around 80% of the distance between MIN-MAX.
Ralf S.