Linc,
First let me say, I notice now that I have two Sent folders for this account, both were empty. When I created my new mailbox in Apple Mail when I switched ISP's in January, it created subfolders called Draft, Sent, Junk and Trash. That must have been when my old Sent folder, which had the same name, went empty. Anyway this new Sent subfolder has never saved a Sent email. (And I think I just figured out that the black dot indicates it's an IMAP account because my other accounts are all POP and they have a little airplane next to them, not a black dot.)
To answer your question, when I was talking to the tech support at my ISP a few days ago, he told me to sign into the mail server from my webmail to see if the missing emails were there. No, that Sent folder was also empty. He had me "subscribe" my webmail Sent folder and now when I send a message from my phone or from Webmail, it shows up in my Webmail Sent folder AND my Apple Mail Sent folder. But when I send items from Apple Mail, it still doesn't show up in my Apple Mail Sent folder nor does it show up in Webmail.
At this point, I am just bcc'ing myself when I use Apple Mail to send messages from the account. Not cool. Any more ideas before I just delete the mailbox and start over?