Show us your current source... it may not be constant.
The discharge pin will not stop discharging the cap until the voltage at trig gets down to 1/3 Vsupply. There is often some rebound in caps, but it gets worse (not better) as they get bigger.
Is the 12V supply regulated?
The electrolytic cap should not be recharging with a curved path unless the charging rate is proportional to the voltage across it (not a constant current).
One idea is that the common mode voltage range of the LF353 is +-11V minimum, given a +-15V supply voltage. That means it can't get closer than 4V to the negative rail (GND in your case), worst case. If you go below that, the JFETs on the input could start sourcing current. If this is the case, measuring it without the opamp in the circuit should change the results.