Sent messages gone from Time Machine

I posted this on the Time Machine forum and they sent me here. I have several issues, one of which is Mail going offline frequently throughout the day when I have not instructed it to do so, and refusing to go on-line when I request it. I have to close the program, reopen it, and it's back on-line. A few minutes later, it's offline again. I read in the Discussions to trash the prefs and re-enter all my account info. I didn't get that far because as soon as I trashed the prefs all my Sent mails were gone. I went into Time Machine to retrieve them and they aren't there. I've tried rebuilding the Mailboxes, no go. I also dragged the prefs out of the Trash and put them back. Still nothing. Does anyone know what I am doing wrong and where my e-mails went? Thanks.