Hi Matt,
In order to find the root cause of the issue, I'd like to collect the following information:
1. Whether other users in your organization have this issue.
2. When did the issue start?
3. If you send an email from the Outlook 2010, whether you can see the emails in the send items of the Outlook 2010 client.
In addition, please make ensure the option ‘Save copies of messages in the sent items folder’ is checked.
In the Outlook 2010 client, click File > Options > Mail > Save messages.
I'll appreciate if you post the results here.
Thanks,
Aaron Yuan