Is there some DC feedback around this circuit that isn't shown?
How about taking the cap out of the picture? Leave the op amp in the "off" mode. Disconnect the cap from the high impedance node and replace it with a high value resistor back to the 6V supply, then set up a scope to trigger on the jump. See if something in the room sets it off. That fet has a 10nA leakage, which would be a mV with 100k resistor, so a volt drop would be
1e8. You probably have 100Mohm handy. You will have to AC couple the scope to get around the drift due to gate leakage.With high impedance driving CMOS opamp, you can detect a piezo igniter going off from across the room. I ran into this with an amplifier being fed with pyroelectric film.
They test gambling machines in the proximity of piezo lighters, just to insure they don't glitch.