The "Share" will stay there unless deleted by the doctors or you.

I guess most doctors probably won't notice that they can delete a "Share". However, since you are sharing a folder from the doctor's account to you, the shared folder and the Share belong to the doctor account, so the doctor can always delete the shared folder or the Share if they want to.

If you designed it the other way as I mentioned before - create folders in your own account and share them to the doctors. Then you have full control over the shared folders and its permissions.