GFCI outlets aren't designed to last forever. It could be that the GFCI simply died when under load.
One thing I would make sure of is that when the GFCI is replaced that it is NOT put in-line with the circuit (i.e. make a pigtail in the box and have the GFCI not use the LOAD side connections). There's generally no reason why a refrigerator should be protected by a GFCI
There's no requirement to GFCI protect receptacles that serve a refrigerator. Unless the fridge is plugged into a countertop receptacle.
My bet is that it was placed in-line by a sloppy contractor or a prior homeowner who didn't know what they were doing. In either case, putting the GFCI outside the circuit should ensure it is never overloaded again.