I'm trying to ascertain as to whether my right analog stick is broken. It doesn't function in the Vita's main menu but it appears to work fine in Uncharted: Golden Abyss.
Only the left stick can be used for menu navigation. However, with Uncharted: Golden Abyss, I did notice that my right analogue stick didn't work at times. Either Drake moved on its own or it wouldn't move at all. To fix the issue, a reboot was required. I think Sony eventually fixed the issue through a firmware / game update.
I believe only the left analog stick/d-pad can be used for navigation in the menus. If the stick works in-game, it's probably fine. Try another game or demo that uses the right stick (For example, Super Stardust Delta) just to be sure.