The car starts up, and the oil pressure, just fine.
But after the car runs for a good while, 30 miles (45min driving), the oil pressure will drop to zero at a stop and my check gauges light comes on.
When I accelerate, the oil pressure picks back up and is fine, until the next stop.

The cycle resets once I turn the car off and let it sit.

What is causing this?
the last oil change was done 2 weeks ago.

I used 10W-30.
The mechanic mentioned no other problems with the car.
I've added Casite Super Oil Treatment to the engine today. Could this help?