Why not check in with the voltnuts in the Metrology section?
Those guys really go out of their way to keep some units under power, e.g. their LTZ1000 references.
For standard use one might want to consider mechanical stress due to temperature cycles. Just keep the unit powered, even if you are using it only once every half hour.
Regarding stabilization: have a look at the manual. My bench multimeter 34470A takes about 90min to stabilize fairly well, so that would be a hint for which expected idle times to switch off.
Additional hint: many manufacturers define reliability by both MTBF and power cycles. (hard drives, light bulbs, ...)