Go into the router's settings and check that the DHCP Lease Time is set to an adequate value. Mine is set to 1440 minutes (24 hours), although the DHCP server *should* automatically renew the lease long before it expires.
In your case, a short lease time might be causing the PC to lose its IP address. When a PC is rebooted, it will request a new IP address from the DHCP server. Alternatively, you could try giving the PC's network adapter a fixed IP address to see if that resolves the problem.