Klaus will have the definitive answer but I can tell you I've used my Khartago both ways. Currently I work from my home with music on all day so my Khartago is never shut down. However I will soon be changing that and may go to the on/off scenario. In the past, I never heard anything bad when I shut it down (as when on vacation, etc.) but did notice that it seemed to need a half hour or so to return to "full song" after. (This is all after full break-in, of course). FWIW, my elderly father-in-law (who pinches pennies) had my Khartago on loan for a few months and turned it on only when listening. He swore there was no difference at all.
Klaus?
UPDATE: This is from the Unified User's Manual available from the Odyssey website
http://www.odysseyaudio.com/"Even after the initial break-in period, the internal components lose their charge each time the unit is
turned off. The full re-charging can take hours (and sometimes days!). Therefore, the best sonic
performance is achieved when the components are kept fully charged at all times. This essentially
means leaving your equipment on at all times--if you are comfortable with that arrangement. If not,
at least be aware that it will take some time for your unit to warm up and fully charge each time you
power up. These charged-based performance issues are applicable to most electronic equipment,
and are especially critical in high-end solid-state gear such as Odyssey amplifiers and
preamplifiers".
So there is the word from the man - and your options.