In short, not really, but don’t make a habit of it. The biggest variable as to the potential harm is whether or not you’ve got a solid-state or tube—particularly all-tube—amp. Some would argue that a solid-state amp could be left on forever without any real damage. Regardless, leaving a solid-state amp on during a gig, including drinking and flirting breaks, is not going to hurt anything. But just for good measure, if the gig is dusty or hot, it’s probably best to shut down.
In my opinion—and this is subjective—the same is true for tube amps, at least as far as gigs go. I would not leave a tube amp on all night, but the average-length gig is no big deal. Tubes are tougher than many think. If you leave the amp on, but with a “standby” switch engaged, there is the risk of “cathode poisoning,” which occurs when the tube’s cathode is hot but not shedding electrons to the plate. I don’t think this would occur to any notable effect over a gig’s typical length, however.
Got something to ask? Need help with the task? Don’t turn to the flask; send your query to bassplayer@musicplayer.com with the subject line “Ask BP.” We’ll try to answer it ourselves, or we’ll foist it off on a genius of our choosing.