Ed,That's an interesting error message. Windows 98 is not very stable, and leaving it on most of the time usually isn't advised. Something more bulletproof like NT or 2000 is a better choice for an always-on machine. Maybe you can work around it.
You have a machine with two NICs in it? Is there a particular reason for this configuration? It's a configuration asking for trouble, because NIC drivers have a habit of conflicting with each other. If you are only using one NIC, disable the other in your hardware configuration, and update the drivers of the remaining one.
My other thought is that the machine has a sleep feature, and when it's waking up it looks for the boot diskette. It's often an OEM thing, not necessarily Windows itself. If so, you can usually disable the sleep feature in the BIOS. Otherwise, look in your Windows power settings. It's good to shut off the monitor and spin down the hard drives, but you don't want it to go into "Standby" or "Hibernate" -- if you have one, use the OEM power utility, not the Windows control panel.
It is possible that it's a hard disk problem. Backup often until you get this resolved!