The issue is most likely one of these two:
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As @Mark_Rocka said, the temperature change in the room can affect it.
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Most likely, the slots in the nut of your banjo are pinching your string. As you tune up to pitch, the string gets hung a bit so that you actually twist the tuner further than it needs to go, but you can’t tell because the nut is grabbing the string. As it sits, the nut slot slowly lets the string tension loosen and the string tuning goes sharp. The best thing to do is loosen your string just enough to pull it out of the nut slot, then lightly clean it out with a piece of fine sandpaper folded in half. That will remove the debris or snags that may be catching your string, but be careful not to file it down and actually lower the string slot depth. If this doesn’t help, you may need to be a bit more aggressive.
One way to tell if this is the issue is to tune your banjo like normal (always tuning from below the note up to the note), then lightly press on the string between the nut and the tuning post. If it makes your string pitch pop up sharply, then that’s the issue.