As to a solid fix, I never found it. Worth a call to Microsoft but if you have PDAs the issue seems to happen more often.
Started noticing this a week or so ago, first one machine, then another, and now two more- close Outlook 2003 by the 'X'in the u/r corner and it stays resident in task manager, as many times as the user opens and closes Outlook. Terminate by 'File>Exit' and it truly stops and goes away. Did some searching and found lots of others with same bug. Clean systems, behind good firewall (Hardware), A/V scanned daily, spyware clean, etc. One of them only ever gets connected to internet a couple of times a week. Considering a Nuke and reload on one of them not heavily utilized. Any more clues? I tried reloading Office after a full remove and reboot. No change. TIA