The comprehensive rules answer many questions such as these.
"419.6b Regeneration is a destruction-replacement effect. The word "instead" doesn't appear on the card but is implicit in the definition of regeneration. "Regenerate [permanent]" means "The next time [permanent] would be destroyed this turn, instead remove all damage from it, tap it, and (if it's in combat) remove it from combat." Abilities that trigger from damage being dealt still trigger even if the permanent regenerates."1. At what point in the end of turn does regeneration shield expire?
2. Do players ever receive priority during the cleanup step?
3. If the cleanup step is interrupted by any means, does it restart?
"314. Cleanup Step
314.1. If the active player's hand contains more cards than his or her maximum hand size (normally seven), he or she discards enough cards to reduce the hand size to that number (this game action doesn't use the stack).
314.2. After discarding, the following actions happen simultaneously: all damage is removed from permanents and all "until end of turn" and "this turn" effects end (this game action doesn't use the stack).
314.3. If the conditions for any state-based effects exist or if any triggered abilities are waiting to be put onto the stack, the active player gets priority and players may play spells and abilities. Once the stack is empty and all players pass, another cleanup step begins. Otherwise, no player receives priority and the step ends."
So shields last until the cleanup step. After it goes away, unless something invokes 314.3 (which does not happen in the situation you describe), no one gets priority, and therefore no one can play activated abilities.
It is POSSIBLE for the cleanup step to restart but something needs to force that.