I also realize that I can back out of the "Lost hub" message, but that doesn't change the fact that I can't control anything after that anyways until I reset the hub.

Nope. The remote will no longer control anything until I power cycle the hub. It doesn't seem to have anything whatsoever to do with syncing - I've had it stop working between keypresses on the remote. It is working normally and then just stops sending anything. At some point after that, it will say "lost hub", but the "Lost Hub" is not the start of the sequence of whatever is actually locking up the hub.