Can the Wonder that pulls from the discard pile be used multiple times?
You can use this ability one time only: exactly at the end of the turn in which this stage is built (not at the end of the Age!).

(And note that it’s not only for cards from the "previously played ages". The discard pile may also contain cards from the current Age and even the current turn.)

The relevant explanation is on page 8 of base game rules, "The Mausoleum of Halicarnassus":


  Clarification: this special ability takes place at the end of the turn in which
  this stage is built.