The long-term problem with being beloved by the GOP faithful but not by anyone else is that the GOP isn't that popular (more people identify/lean as Dems, and more still as Independents) and skews overwhelmingly older. The crew may support the captain of the ship, but the ship is gradually sinking in the sea of demographic change.
Someday we'll see Corbyn/Labour situation where the party stalwarts are fiercely supportive of their leader - but the party has shrunk to the point where it's incapable of affecting anything.
Sadly for the country, though, right now is not "someday."
Best we can hope for in the immediate future is to chip off more old-school GOPers and turn them into Independents (which happened a lot during the latter half of the W era.)