You can see the mail transferred in the mailbox.log file.
Code:
2009-10-01 11:41:25,950 INFO [btpool0-41449] [name=fonz@domain.com;mid=304;ip=192.168.3.199;ua=ZimbraConnectorForOutlook/5.0.3064.18;] soap - SyncRequest
2009-10-01 11:41:26,094 INFO [btpool0-41449] [name=fonz@domain.com;mid=304;ip=192.168.3.199;ua=Zimbra-ZCO/5.0.3064.18 (5.1.2600 Service Pack 3;; en-US);] mailbox - FileUploadServlet received Upload: { accountId=122ef691-aa88-45b7-bd11-7003dded6b9e, time=Thu Oct 01 11:41:26 CDT 2009, uploadId=9b0361a4-b6da-4623-889b-7557255f8f71:a1c2b6c5-89d7-45e2-8323-0c3cee3f046a, lslib32.bin}
2009-10-01 11:41:26,132 INFO [btpool0-41449] [name=fonz@domain.com;mid=304;ip=192.168.3.199;ua=ZimbraConnectorForOutlook/5.0.3064.18;] soap - AddMsgRequest
2009-10-01 11:41:26,133 INFO [btpool0-41449] [name=fonz@domain.com;mid=304;ip=192.168.3.199;ua=ZimbraConnectorForOutlook/5.0.3064.18;] mailop - Adding Message: id=1657, Message-ID=<1F2C13C581BA40F0ACCEAAFD12078226@DOMAIN.COM>, parentId=-1, folderId=5, folderName=Sent.
2009-10-01 11:41:26,176 INFO [btpool0-41448] [name=fonz@domain.com;mid=304;ip=192.168.3.199;ua=ZimbraConnectorForOutlook/5.0.3064.18;] soap - SyncRequest If you're not getting that, then the problem may lie with the Outlook Connector, Outlook itself, etc.