Jimbobb , I can't tell you exactly what's wrong , but I have experienced this myself.
I can tell you that it is a bug. For some it never shows. For others like you & me it does. (Some maps more than others) However , even though there is no known fix....
I have noticed that after a few hours of gameplay , it magically disappears ,and helicopters sit nice and stable.
(Even after game is closed and restarted another day, the bug shouldn't reappear)
WARNING: If you change certain settings under Dynamics it seems to restart the bug ,but after a while of playtime ,the bug disappears again.
I know this doesn't make sense ,but I have done trial & error with this bug many times ,and it's not a coincidence of timing. It doesn't seem to matter what settings are set to ,just as long as they are left alone once the jumping stops.
Hope this helps ,
Powerstomp
P.S. Anyone want to fly multiplayer ,private message me & I'll be glad to host.