Foul Ball Rule: Must Runners Re-Tag After a Foul?

Question
If a foul ball is hit, must the runner on base "re-tag" his base?
Situation: Man on 2nd base leading off, the batter fouls one to the screen (the foul ball is not caught by a defender). Does the baserunner need to retag the base or can he remain off the base until he decides to advance?
If the baserunner is required to re-tag his base, at which point do you request the umpire appeal?

Answer
Hi Tad,

yes, a runner should always tag up after a foul ball is hit.  Its good practice and it will ensure that the runner can advance.  Even though a foul ball is 'dead', it's good practice for the runner to tag up.  Without tagging up, the runner cannot advance before touching the time-at-bat base.

At least, that's what I was told.

JohnMc