It seems that the Option "Save copies of messages in Sent Items folder" , is not selected in your outlook. Check whether it is selected or not. If it is already selected, try to follow some simple steps as given below:

1) Open Outlook
2) Go to Tools Options and then E-mail Options
3) Unchecked the box next to "Save copies of messages in Sent Items folder"
4) Save your changes
5) Exit Outlook.
6) Restart your Outlook e-mail application and repeat the above steps, this time you need to put the check back into the box you unchecked before and save your changes.
7) Try to send an email and check whether it appears in Sent Item folder or not.

I hope above procedure will help you to overcome the problem.