One of my LORs came from a prof who said he submitted the exact same letter two years in a row-he only changed the date on the top. He told me he was doing this before he sent them in to AADSAS. This played on my nerves but ultimately worked out for the best. As long as the LOR is strong, you should be in the clear. Of course, some schools keep files from prior years and presented me with stuff from both applications at the interview. This seems like it should be pretty rare, but it happened to me.