In case people wonder what sort of a tyrant I am, I invoked the extreme of a Timestop model exactly because it should help people realize exactly how many people are affected by this "agency" of someone ignoring one player and all other players connected to that second player, and all events engendered.
It's serious enough to perhaps have a policy in place telling players to report immediately when someone is unable to respond to info requests beyond X days. For instance, report after 5 days, staff will look into it, after another stretch they may be forced to intervene. Adjust day count to be both useful but understanding that we don't always log in or read @mail every day.