Op-Amp as comparator for driving relay stops working after short time
There is a potential for relay coil current to commutate through a path you don't want.

Turning the coil is no problem, note the current path shown in red below,


Turning the coil off is where the problem can occur,


What you want to happen is for the coil to decay through your flyback diode (yellow loop). However if the ESD/substrate diodes of the opamp have a lower forward voltage by 10's of mV they will hog all the current and potentially latch up the opamp (blue loop).

When you run a bi-polar opamp as a comparator it can no longer drive a 4-quadrant load (reactive elements). You are forcing either the high-side or low-side output element to be on (driving the output high/low). The problem here is that the low-side element can only sink current not source. So if you need to source current at a low output voltage, the kickback from the coil forward biases the substrate diodes. This is in contrast to when you run an opamp in closed-loop, it will drive the output stage as needed (source or sink) to maintain the desired output voltage. 

Solution

Add a diode in series with your opamp. This ensures the coil commutates through the flyback diode, not the substrate of the opamp.