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How long is "a short time"?
There are other settings than "turn off monitor": there are also "sleep" settings. If you have that set to, say, five minutes' worth of inactivity, that would explain a blanking-out monitor (no stimulation = all-black "image").
Check your power options and set the "sleep" options to something more reasonable, like an hour's worth of inactivity. Truth be told, a computer consumes LESS THAN ONE CENT'S WORTH OF POWER per month. Your power hogs are your HVAC, washer/dryer, and old-style oven/range.
Secure remote assistance costs money, yes. I'm afraid that it takes effort to set up and also consumes experts' and administrators' time.
You don't really need remote assistance IMHO for this. You can readily check out your Power settings from the Control Panel (the ol' "Windows button") and fuss with the various power-saving and sleep options.
Bear in mind that SOME power-saving options may be associated with the monitor hardware itself--accessible only through buttons on the physical monitor--and a remote session cannot access those controls.