Do these deleted emails go into your Deleted Items folder? Do you have any
rules applied that would cause this behaviour? Or is it something simple like
filtering your view? If you're only seeing mail from the last 7 days, this
could be the issue.
In your Sent Items folder, click on View > Current View and make sure
Messages is what's ticked. If this is not the case, please post back with
further details such as your version of Outlook, type of mail account, any
error messages and/or numbers, etc.