--- Begin quote from "fiddlewood"
Without knowing what weight distribution you have on your banjo it's hard to tell.
Where is the balance point on the instrument? Some banjos have lighter pot assemblies and heavy necks (such as less expensive Kays etc.) If this is the case with yours another strap may not fix the problem.
If I grab my banjo where the head meets the neck and lift only the neck comes up (this is with most). The point where it balances is only a couple inches from the center of the center of the resonator, so I can put the neck at whatever angle I choose and it will stay there until I move it.
--- End quote
I'll have to double check that when I get home tonight. My banjo is older and the neck seems longer than usual. It may be that the balance breaks that way too much, causing the head/neck to slip downward while playing standing up.