Why do the emails in my inbox disappear after I have closed and then re-opened the mail program?

I have used Windows Live Mail for years with no problems but recently, when I open the program and read my mail, I delete some and leave some to refer to later (like my airline reservation information for an upcoming flight).  The next time I open the mail program, the old emails are there for a second or two and then disappear.  Why? And where did they go?  They are not in my deleted mail folder.