Well, that seems to be a DNS issue. If you're using the same DNS server address on the laptops, and other laptops are connecting through the same WAP successfully, it would seem it's something on that machine.
Since reloading Windows seems to fix it for a short time, it seems this is something that the user is loading on the machine. When the wireless ceases working, does the laptop still work normally if you connect it to a wired connection?
On a non-working machine, try this stack repair and see if it changes the symptoms.
TCP/IP stack repair options for use with Windows Vista.
Start, Programs\Accessories and right click on Command Prompt, select "Run as Administrator" to open a command prompt.
In the command prompt window that opens, type type the following commands:
Reset WINSOCK entries to installation defaults: netsh winsock reset catalog
Reset IPv4 TCP/IP stack to installation defaults. netsh int ipv4 reset reset.log
Reset IPv6 TCP/IP stack to installation defaults. netsh int ipv6 reset reset.log
Reboot the machine.