mail deletes messages once they are read

Mail now deletes messages once they have been read. I did not choose to delete them; they simply disappear. They are not in the trash. They are not in the mailboxes. They are gone. I have received some general advice on how to check my mail program, which I'll follow. But I wondered if anyone else has had this problem.

I deleted my mail PList in an effort to solve another problem, so this is a "clean" version of the program.