It is most likely that the wireless adapter in the PC is losing its IP address, which could be due to interference with the wireless signal.
Make sure you have no mobile/cordless phones located near either the router or the PC (WiFi adapter). Also avoid close proximity to large metal objects, in particular central heating radiators.
Try changing the channel number in the router, which is probably using the default "11" unless you've already changed it. Try something like "8" or "6".
Also allocating a fixed IP address to the wireless adapter might help to keep the connection active. This needs to be in the same subnet (IP address range) as that used by the router. For example, if the router's IP address is 192.168.1.1 give the adapter the addresses:
IP address 192.168.1.2
Subnet Mask 255.255.255.0
Default Gateway 192.168.1.1 (the *router's* IP address)
DNS Server address 192.168.1.1 (the *router's* IP address)
The first two 'octets' of the router's IP address will almost certainly be 192.168 so just make sure the third 'octet' you use matches that of the router. The final 'octet' can be anything between 2 and 254.