If this is a power save mode, then this computer has problems. Keyboard OR mouse should wake it up, but if it's needing a reboot, then something is eating resources.
If I were you, I'd run MSconfig and check selective startup, then go to the startup tab and remove the checkmarks from everything except systray and explore. Systray and explore are needed by Windows to run, everything else does not need to load when booted. Save this and shutdown (manually). Then start it back up and wait and see if it happens again after 20 minutes.
If it does not happen again, then one (or the combination of all) of the programs loaded at startup, just palin eats too much of your available resources.
If it does happen again, then I'd backup and offload all the data from this computer and totally wipe the hdd and start over with a fresh new Win98 install amd go from there. If it still happens after this, then look into RAM, Video, Overheating, and/or possible systemboard issues.