I suggest resoldering the connections to the frequency determining
components. If there are any mechanical linkages or bearings, those could
be needing some cleaning and/or lubrication. Especially look for wiping
contacts that could have a thin film of corrosion.

If it's permeability tuned, there are no wiping contacts. But the slug
could be loose or dirty.

Look for cracks in capacitors that could cause capacitance jump with
temperature or movement.

Measure the supply voltage on the oscillator; if it changes when the shift
occurs, the trouble could be caused by a zener diode.

I could go on, but you get the drift. (that;s a pun)

73, Bob