A number of our customers often come to us and say "my banjo won't stay in tune". Let's disregard all the jokes about not being able to tune a banjo. Modern banjos with geared tuning pegs will stay in tune. The fix for this is a very easy one. 99 times out of 100 the problem is simply that the screw which holds the tuning peg has become too loose.
To fix this you just need to tighten the screw which runs through each tuning peg. Don't crank down the tension. We still want to be able to move the tuning peg. There should be some resistance though so that the string tension doesn't just pull out of tune.
Try this quick fix. If this doesn't solve the problem, then we can check a few other items such as the bridge being in the right place, the tailpiece fastened securely, and the neck fastened securely to the pot.