Hi,
Please confirm that there is no related Outlook rule created in Outlook to move the sent message to other folders or remove the sent items. In Outlook 2013, please click File > Options > Mail, in Send messages part, please check whether the following
options are checked:
Save forwarded messages
Save copies of messages in the Sent items folder
If the send message settings are correct in Options, in Account Settings > More Settings, please uncheck using Exchange Cached mode, and restart Outlook to use Outlook in Online mode. Then check whether the issue persists.
If the issue persists in Online mode, please restart Outlook in safe mode to have a try. If the issue doesnt happen in safe mode, please come back to Cached mode and disable the added third-party add-ins one by one to determine which one is the cause of
this issue. About how to start Outlook in safe mode, please refer to:
https://support.office.com/en-za/article/I-can-t-start-Microsoft-Outlook-2010-or-2013-or-receive-the-error-%E2%80%9CCannot-start-Microsoft-Office-Outlook-Cannot-open-the-Outlook-Window%E2%80%9D-d1f69da6-b333-4650-97bf-4d77bd7abb85
Regards,