Comparator circuit undesirable fluctuations
You have hit the phase-reversal problem. Your lower rail input is limited because of the current source there. There are many techniques to fix that. The easiest is to limit the input voltage such that you do not close to the rail that is sensitive. For this you might need to switch your N-FET diff pair into an P-FET diff pair, if you have to work close to GND. Another way is to design a rail to rail input stage.