I hate those kinds of problems, they can be a real pain.. Some things I've found to look at are
1. Is the router bad? I have seen routers, especially linksys go a bit flukey.
2. I have had electical issues mess stuff up. IE voltage drops or heavy loads on lines running alongside network cables.
3. I had one client who had sporadic problems.. Turns out they were putting their laptop transformer right next to their wifi card at times.
4. Check the lease times on the DHCP. Can you set it for one week?
5. I have had situations where the DHCP leases need to be cleared out on the server. I forget exactly how I did it, but old leases were using up all the ips available for leasing.
6. Any IP conflicts? ie. someone coming in with a laptop that is hard wired to one of the dhcp addresses.
7. have you tried rebooting everying including the servers, routers and switches?
good luck with it.