Runner(s) lead off on every pitch (typically), do they need to return and touch base after each ball and strike? I can only find reference to having to return to, or be in the vicinity of the base on foul balls.
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There is no rule that they have to retouch. They commonly do so to avoid being picked off.
As Navy said, there's no requirement to return during a live ball. When the ball becomes dead (foul ball, for example), they are supposed to touch the base and remain on it until the ball is live; however, the spirit of the rule is to prevent a runner from getting a huge lead-off with no jeopardy of being thrown out. Because of this, as long as they're near the base, an umpire will allow it.