Should preamp be left turned on?

I'd leave it on unless there was a danger of electrical storms, in which case I'd switch it off and unplug it. Otherwise I see only benefits in leaving it on ... longevity, sound (maybe), and no downsides (unless it's got a huge power consumption, which is very unlikely).
I leave my integrated amp on all the time, but I turn the volume to minimum and select an unused input when it is not in use.

Yes. I have the same.

I've been leaving ss electronics continuously powered up for 35 years through three systems and have yet to need a repair.

I second SeanDTaylor: Longevity is a benefit only for low power - which a preamp is. For high power Class A or tube amps, this point would be ambiguous (Pass X600 springs to mind). I leave mine on all day and off only at night as, what I feel, is a balance between thermal loading and thermal cycling. Arthur

I've heard it said that SS should be left on and tube should be switched off.
The reasoning was that SS takes a long time to warm up, and that thermal cycling causes expansion and contraction that can break components (e.g. causing electrolytic caps to break and leak).
Tubes, on the other hand, wear out the heater element if left on all the time, and warm up very quickly when switched on.
I have only ever owned SS and never class A so the electricity bills have never been a problem.
I suppose a fireman, sorry, firefighter, would tell you that all electrical equipment should always be switched off and unplugged when not in use. I wonder what an audiophile firefighter would say? :-)