Probably a dumb question, but when you turn a character's stealth off to use powers like perplex and probability control on friendly characters, when can you turn your characters' stealth back on again?

If you cancel a power or ability, then the power or ability will return at the end of your turn.

If you simply choose not to use a power or ability at the beginning of an action (for example, many special powers says a character "can use X" and you can just choose not to use X), then that choice only impacts the current action; with the very next action you could choose to use that power again, if you wished.