What causes a heat pump to short cycle?
It’s several years old, never had a problem, so the problem is not a mismatch between the size of the house and the size of the pump.
Clean the air filters is first. then change the thermostat. What’s the next step if those 2 don’t fix the problem?
Does it have enough freon in it? Can you get inside and look at the coils? My guess is that it’s low on Freon or the coils are plugged with cat hair or something like that.
I would start with figuring out why it’s shutting off. It’s either a high pressure switch or a low pressure switch, or the thermostat itself. High pressure would be cause by low airflow across the coil or a restriction (kinked line). Low pressure is likely low freon. The thermostat could be something as simple as improper thermostat location, with air blowing across it.
I doubt it’s the thermostat though, as short cycling switches are incorporated into them, like a 5 minute timer. How short is short anyway?