Our window unit's grill freezes over at least once/day.
I have continually cleaned the filter, and gave the grill the time to thaw and dry.
But still it happens.

??

If the outdoor temperature is to cool many times a window unit will freeze over.

OR

The evaporator could be dirty

OR

The unit might have a small leak and be a bit short of refrigerant. It does not take much of a leak on a window unit to cause this problem.

If the coil, is not dirty sounds like it may be time for a new unit.