I think not. You could replace the battery or just remove it entirely, if your use case is "always on". The GPS is not doing any warm starts anyway.
There are only few things that "wear" on a GPSDO. One is the oscillator itself, OCXO's have a limited service life,
Or it could be the antenna or cable. Eventually, moisture will creep in.
Are there no diagnostic outputs that you could use apart from a few LEDs?