12-16-14: Melbguy1+1
To summarize, there are no hard and fast rules. The benefits of keeping a (solid state) amp switched on all or most of the time vary from amp to amp. But rule of thumb, large amps with oversize power supplies and filter banks will generally benefit more from being left on as it takes the psu's longer to warm up and reach optimal thermal conditions.
It seems to me that the responses so far have generally not given adequate focus to the specifics of the OP's amp. He has not indicated what specific model it is, but perhaps it is one of the three integrated amp models in the Moon Neo series, which the manufacturer recommends be left on continuously. These are described as providing a standby mode, but apparently all it does is to "disengage the input section from the rest of the circuitry." The three models operate in Class AB, and have 8 ohm power ratings of 40, 50, and 100 watts respectively, and twice as much into 4 ohms. AC current draw is not specified, at idle or otherwise. Shipping weights are specified as 20, 22, and 28 pounds respectively.
The OP might consider asking the manufacturer how much AC current or power the specific model draws at idle. It could be that it won't be a great deal more than is drawn by many source components (which many audiophiles leave on all the time), especially if it is one of the two lower powered models. On the other hand, though, consistent with Melbguy's comment that I quoted, given the relatively light weight of these models (relative to their power ratings and class of operation) I suspect that the sonic benefit of leaving it on all the time will be minimal.
As far as the safety issue is concerned, it's hard to disagree with what Schubert and Minorl have said. On the other hand, though, if it can be determined that the AC draw is low at idle, and if nothing on the amp seems to be particularly warm when it is idling, leaving it on all the time would seem to be relatively low risk compared to many other amps.
Regards,
-- Al