Question: My Exchange Server 2003 (running on Windows Server 2003) fails at around 04:54 on a regular basis, though not necessarily every day.

By "fails" I mean that my colleagues try and check their emails and Outlook says "outlook is not connected to exchange." Since outlook tries to update the email every 3 minutes or so, and it records the time when the folder was last updated, it is possible to see the time of failure.

It is impossible to download emails until the server is restarted. Thereupon everything works well.

I have looked in Scheduled Tasks and can't see anything pertinent.

Does anyone have any ideas?

Answer: 
Are you still able to ping the box after this happens or does it become completely unresponsive? Any backups running during that time? Is this server a dedicated Exchange server or does it have other functions?

Otherwise, I agree witi Itai, you should cross reference the the event logs with the time in which your machine goes down. You may also need to get a dump of your system and post any pertinent information here. If it is just exchange that is failing and you still have access to your system, check Task Manager to gather what processes are running during that time.
Yeah, SP2 might do it. If you still have issues, Google for "exchange 2003 sp2 hotfix" and see if any of them are relevant to your problem. Another workaround is to set the Exchange Information Store to automatically restart after a failure in services.msc (if that's the service that's failing), but this doesn't fix the root cause of the problem.