Are you connecting through a wireless hub? Windows might not be turning your wireless radio on after it comes out of standby.

Right click on My Computer > Properties > Hardware > Device Manager > under Network Adapters right click on the one that says "Wireless something or other" and go into Properties > check for a Power Management tab and see if you can untick something to the effect of, "Allow the computer to turn this device off to save power". If you can't find that particular setting check under the Advanced tab. Most newer Intel drivers have all their wireless network settings listed under Advanced.

It could also be a problem with your router's DHCP protocol not assigning your machine an internal IP after standby. If the above doesn't work you can try setting a static IP for your machine.

Does the problem you described happen when you are connected to another wireless hub elsewhere?