My name is XXXXX XXXXX I'd like to help you with your network sleep issue. As I understand it when you wake up your computer from sleep mode for a long time it has trouble reconnecting to the wireless network.
This is a common problem, but it can have many different causes. We know it's not your router because you said that other machines on your network don't seem to have this problem. So the issue is with your computer.
Below is a link to website with a procedure I'd like you to try, many people seem to have had good success with this resolving their issue. Let me know how you make out, and please don't forget to push the green "Accept Answer" button so that I may be paid for my service. Thanks.