Well, I am just guessing here, but it might be impossible now to retrieve the letters your professors have submitted. May be I am wrong. It depends on what online app system the school is using. Perhaps the fact that it is expired means that everything you had uploaded was deleted from their system. The truth is - only this school can tell you what has happened with your recommendations.
If I were in the same situation, I would perhaps ask my professors to resubmit letters and not tell the school about the situation. But since you have already written an email to the program all you can do is wait for a reply. Or perhaps you can also call them to expedite the process.
Good luck!