If I were to turn stealth off on a Batman ally (say, in order to prob or perplex them), when would stealth reactivate? Am I turning off the TA, or am I turning off the stealth that the TA grants? In other words, does stealth return at the end of my turn or the beginning of my next one?

almost positive its the beginning of the next one
someone more knowledgible in team abilities will answer better than i though

If you option off stealth it returns at the end of your turn, so your bat ally would return for your opponents next turn. You have to declare you are optioning it off before you make an attack roll, or before you try to probability it, if not then you would not be able to perplex or prob.

You can choose whether or not you want to use Stealth on an action-by-action. It is perfectly legal to not use Stealth in order to be Perplexed, and then use Stealth when you attack as your next action in order to protect yourself from being PCed.
This only applies to abilities you use, not the ones you possess - a figure with Stealth on its dial can only deactivate it for the remainder of the turn.

Thanks guys. I figured the TA stealth should be better, not worse, than dial stealth. That makes more sense to me.

For clarification, Quebbster is right.... but the other two used to be right.
Before the LoSH rulebook, Batman Ally had the same script as stealth... you could turn it off and it would return at the begining of the next turn. However, the LoSH PAC changed it so that Bat Allies could USE stealth (made the script MUCH easier, plus it allowed for a couple technicalities that made it easier to use). Now, you can choose to not use the power (as Quebbster said) and you can choose to use it again with the next action.

hmmmmm! I had a judge rule a few weeks ago that when i turned off the Bats TA so a fig could be perplexed/PC then that character did not have stealth/Bats TA return until my next turn. so you're saying that is incorrect?

that is incorrect. if you turned off bats TA it would return at the end of the turn in which it was turned off. however, as the other gents have said, in most cases it is more beneficial to choose not to use the stealth rather than turning off the TA.

This is right. It's more of a technicality of the wording (turning it off vs not using steath), but before the change to the script, turning off the TA was the only option.... now you can just choose to not use the stealth that you have the option to use.