If I am correct: A pump with a rotating impeller would have wear issues from running dry and the transfered heat from the motor will have contributed to the issue. Ran in to this on many boats fresh water systems over the years. Get new impeller and plate and gasket. Clean armature too (see below).
AND use this type of pump as your back up...replace it with the diapram type, less problems in the long run.
With the newer style diaphram pump there shoudn't be an issue other than the armature and brushes may be a bit discolored/tranished which acts as a non-conductor and will impede smooth operation of the motor. this tarnish come over time and incidents like yours. It is easy to pull all of it apart, ususally pull of the pump head 3 to 6 screws then 4 long rod screws/bolts to slide out the armature use a very fine emery cloth to clean, maybe lube the bearings if you can and slip it all back together...Voila it works better! BTW clean the diapram while it is off too...soap and water should do the trick.
There you go. Which type do you have?