We have a small peer-to-peer network server in our office - 5 work stations (Win 7 Pro), two networked printers and a WAP.
Somedays, when opening Windows Explorer or the "Network" icon on the desktop, any mapped drives on the server are visible but the server itself is not. This seems to happen randomly on different workstations. Somedays, the server is completely visible from the work stations, but other days, not at all.
(by the way, the server is still running Win XP Pro with two hard drives set up in an RAID 1/ mirroring configuration.)
Also, we do not use a domain. Our network name is just our company name - a single word.