Some teachers receive a single entry visa. This visa allows the instructors to enter Korea only once. If you plan to go abroad during their contract period, you must go to the Immigration Office and pay a fee to have their visa changed to multiple entry status. (Note: Americans are usually issued multiple entry visas automatically when the E-2 visa is stamped into their passport but please confirm with the Korean Embassy or Consulate).
We're not sure why this happens. You might ask for a multiple entry work visa when you apply. Can't be sure that this will work, but it certainly can't hurt.