Perhaps the capacitor is holding a charge if it has only the comparator input to leak through. You show a resistor there, but the value of the capacitor, nor resistor is shown in your schematic, and yes, no rectifier either.
Another possibility is the comparator is latching up, which (with some comparators) can occur if the input voltage goes outside the voltage powering it.
If all you have is a rectified AC signal feeding the comparator (with no capacitor), even a large amount of hysterisis is not likely to prevent 50/60 Hz oscillation. I'd be suprised in your circuit doesn't oscillate at all times after the threshold is exceeded.