Realistically, they will lose fans until and unless they return to winning.
The Phillies have a core of fans who will support the team regardless of how they perform. That core's been there for decades - since long before the good days of the '00s, or the good days of the '70s-'80s. But that core isn't all that large.
The rest of the fans come and go, with the team's performance on the field. Not with what the front office does or does not do; most of this group of fair-weather fans really don't understand how front offices work (or care, for that matter). They just want to follow and root for a winner. Nothing wrong with that; it is what it is. But sacking a hitting coach, or a manager, won't really affect them much.
