Shared workgroup computer disappears.

I have 3 computers (2 desktops and 1 laptop) that I am sharing files with.
One particular computer, after a few hours, "disappears" when I try to
browse the computers on the workgroup. I can use the printer that is
connected to the computer, I can map a drive to a particular folder on the
computer even thoughi t is not present in windows explorer or my network
places. If I shut the computer down and reboot, this computer "appears"
again.

Any thoughts as to what is causing this? The OS on the desktops that I
cannot browse periodically is Windows XP Home Edition, and the other is
Windows XP Professional. Both have ZoneAlarm's free version. The router is
Westell's versalink, thought the same thing happens with my linksys router.

BTW, my laptop has Windows Me and no firewall currently.