SQL Server Agent Headaches

An email I sent to some collegues recently:

I'm not real clear on what duties your job encompases, or what
experience you have with server environments, but I thought I would pose this issue to you to see if you had encountered it or know what the fix might be...

I've had SQL Server on two machines now at Work (OSes: Windows 2000 Server and Windows Server 2003). SQL Server Agent (which manages scheduled backups) will occasionally (like once every other month or so) just stop running, and thus, the backups stop running.

This has happend on two different servers over a range of patches and service packs to SQL server, and it is a truly annoying problem (because you usually don't realize it quit running until it's too
late).

Have you ever seen/encountered this problem before, and if so, what can I do to fix it?

I have a sledge hammer and I'm ready to use it.