I had thought that it might be related to the SATA disk I had just installed, but the system still went into stand by in Linux, and if the timeout was less than 10 minutes, so that didn't really make sense.
Now, I have learnt that it was caused by Microsoft's security patch KB835732.
Installation of MS04-011 (KB 835732) broke the S3 Standby
(suspend-to-RAM) timer on my system running W2K SP4. After
installation of the hotfix, the timer under Control Panel -> Power
Options -> Power Schemes (tab), "System standby:" would work if set to
5 minutes or less. The timer failed if set to 10 minutes or longer.
The timer for "Turn off monitor:" continued to work normally; that for
"Turn off hard disks:" was erratic. The system would still go into
standby via Start, Shut Down..., Stand by.
Event Viewer, as usual for power management (PM), showed nothing. I'm
unaware of any tool (resource kit or third party) to troubleshoot W2K
PM.
Uninstallation of the hot fix restored full standby timer
functionality. Reinstallation of the hotfix broke the timer again.
Sure enough, removing that patch fixed the problem. As of this time, Microsoft has not acknowledged this problem with the patch, but its problems are mentioned on The Register.
Update (6 June 2004) This problem is mentioned on Annoyances.org, but without a solution yet.