1. Check to see if sent messages are being set to Expire after so many days. Go to File, Options, click on Mail, and scroll down to Send messages. See if Mark messages as expired after this many days is checked.
2. Is AutoArchive enabled? Under same Outlook Options window, click on Advanced (on left menu), and click Auto Archive Settings.
If both of these features are enabled, Sent messages expire after so many days then AutoArchive deletes them..
If all else fails your workplace may have a retention policy in place that removes them automatically (if using exchange/O365 as your backend email solution)