I'm wondering this too. None of them are frozen, I'm active every day and always have money to pay the board yet somehow they keep getting kicked from the same centers over and over

It could be one of multiple things: One it could be a bug. Secondly, it could be people downgrading their memberships and the game is catching up ((for example, I cancelled mine but it is still go through up to a certain point, when that is done? everyone will be kicked from mine)) or Thirdly, people are upgrading their training centers, your horses' tier is too low and thus getting kicked. Fourth, do you actually HAVE enough money on hand or in the bank to pay for their boarding too? Fifth are you sure you are active daily or at least none of your horse's have 0 health? These are rules set up if you are inactive for X amount of days or your horse reaches 0 health, then they will get kicked out.

Do you happen to know what the pop up says when this happens? Like is it a downgrade or something else entirely different?

All are pretty valid but lets be real, the big one is probably because we all canceled our subs so they are all slowly ending leaving little to no boarding available 

For me it doesn't say anything they are just In Transport

Have you looked at your notifications to see if anything is there? At times the notifications bugs out and sometimes going to the Bell icon to double check stuff shows up there, if there is nothing there, then that makes things slightly more difficult to pinpoint down the issue as I mentioned there can be a litany of issues at play.

Are you re-boarding them at the same place? You could try boarding them at a different place