Speaking ASA....

Rule 3 Sec 5-E1 EFFECT:
".....Umpires should uses discretion as to the intent of the rule concerning player safety."


Is there any instance during a live ball, that once a player has reached base or is running the bases they can remove their helmet not be called out?

Bill,
Technically and absolutely, the answer is no, a player may not deliberately remove their helmet during a live ball without being called out (over the fence home run is not a live ball). That being said, on very hot & humid days I have "not seen" a player standing on a base remove a helmet when all action is done. I've also gone up to that player and said something like "I did not see you take that helmet off during a live ball. If I had seen that, you'd have been out. Please remember to ask me for time before doing that again. And remind your teammates of that too." This is said in a way that nobody hears me except that particular player. That's the discretion the book speaks of. Since I only work the older levels, I prefer the NCAA's wording on this. Under NCAA's rules, that player standing on the base is allowed to remove the helmet when no play is happening during a live ball.

Steve M

And for those working NFHS
 

A player is not called out for removing a helmet during live ball. It calls for a team (coach) warning with any subsequent offender being restricted to the bench.
WMB