The propensity of TV to lock machines on session end is a common frustration here. It seems totally random. Sometimes it'll lock, and sometimes it won't. It can be argued that it is a security feature, but one that is totally inconsistent. Of course, the result of the lock is that you end up getting logged out on the machine you're connecting to, so when you reconnect, you have to log back in. No, it's not an "all or nothing setting". It's totally random, and there is no "setting".
Best I've managed to figure out (and I don't know if this applies to iPhone/iPad), is that the disconnect "X" in the control bar at the top will be marked with a little padlock if TV has randomly decided to lock when you end that particular session. You can pull down Actions and tell it not to do that. But you can never tell when it's going to want to do it.
As far as I know, it is a complete mystery why TV sometimes decides it wants to lock on session end. When I started using TV a few years ago it seemed to want to do it half the time. Now it only does so rarely.