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Live Mail is now outdated and may experience problems. I would download Windows Live Mail 2011, the problem should be resolved. There are also many other email clients to choose from, if you wish. Top 11 Free Email Programs for Windows - About Email
If you do not want to change, try this Bring up Live Mail
Upper right go to accounts>properties>advanced
Check deliver. Does it say leave mail on server.
Note: I checked the procedure on Live Maill 2011, it may differ on yours, only in location of the area to check.