Why does the Windows XP Task Manager icon disappear from the tray?

Why does the Windows XP Task Manager icon disappear from the tray?

One of the more annoying bugs in Windows XP is the tendency for the Task Manager icon to not show up in the tray (aka the notification area). Sometimes it does, sometimes it doesn't, and it's not consistent enough to have an obvious cause. Looking on Google turns up a bunch of forums that have the same problem but no working solution.