Its bad for a guitar neck if its off for longer than a day or two...

the reason being that the massive change in pressure on the neck will warp it no matter what you do.
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If you're going to leave the strings off for an extended period you should also loosen the truss rod, otherwise you'll come back and your neck will be bent backwards with a big hump.
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why the 2 threads? delete one
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Guitar necks have come on alot in that it won't bend in a couple of hours, but yeah, you shouldn't leave it off for more than a day really.
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Yes, you can leave strings off the neck, AS LONG AS YOU MAKE AN APPROPRIATE TRUSS ROD ADJUSTMENT.

For example, Keith Richards usually only has 5 strings on his guitar, he leaves the low e string off. However, if you mean taking all the strings off, that's probably not a good idea.