Everything works as expected if I power the circuit via the ISP programmer (Arduino UNO) or my bench power supply.

But if I use the 3,3V regulator from the PIR-module, the circuit behaves strange. I also tried a L78L33AC regulator powered from the 12V rail, resulting in the same strange behaviour.

My circuit consumes less than 10mA, which both regulators should be capable of.