These solid-state electronic devices are not like a mechanical device, like a car engine or something, that needs occasional running to lubricate the internal parts with oil.
Letting those Moog synths sit powered on, under a cover or not, serves no useful purpose.
The best thing you can do, is to power them for about 10 minutes, once a month, whilst manually moving all those potentiometers across their full travel many times over, and flip all the switches back and forth and play all the keys several times over, to remove some traces of oxidation and corrosion, by way of mechanical friction, that might want to build up on those contacts and carbon traces.
Of course the very best way to maintain those fantastic machines is to...actually play them ! (but you already knew that, right ?
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