Good quality contactor coils are designed to be "go/no-go" with regard to under voltage conditions, in that they will not pull in if the voltage is below 80%, but will not drop out until it is below 70%, so that makes them hold in longer, then not re-energize while the voltage is still low. So for this type of damage to occur, the voltage would have to be low, but not TOO low, for a long time, as in long enough for you to have detected it (assuming the system was designed to protect against voltage sags).
A more common cause of problems that end up looking like that is rapid opening/closing of the control command. For example a tank pump-up float switch acting directly on the coil without some sort of designed hysteresis in the system. Outflow from the tank will result in the float dropping, turning on the pump, it pumps, raises the float, which immediately stops the pump, but liquid is still flowing out, so the float drops, starts, stops, starts, stops ad nauseum, all taking place in a matter of seconds. Eventually the OL relay should trip because this is damaging the motor too, but often the contactor coil will fail first.
So if you have no other evidence of long term voltage sag, I would be looking at your control circuit very carefully. Sometimes even if it was designed correctly, a failure like this is secondary to another failure further up stream in the control system.
"You measure the size of the accomplishment by the obstacles you had to overcome to reach your goals" -- Booker T. Washington