How about accessing the router's software and setting the router the way you want first? For example, I have a Belkin wireless G Plus, so I enter the following address on Safari: 192.168.2.1
This gets me to the router's settings. Under LAN Settings, I set the Lease time to "Forever."
I also make sure that the Connection Time box is not check-marked. If you have set your router to Wireless, then read the instructions next to each setting you decided to choose or change. The OS is that last thing I would think as being the problem. You can test your network by trying another computer.
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More than likely your problems are related to your modem, router, network, or ISP. The computer usually doesn't drop-off; something in the network disconnects the communication. It's also possible that some of your neighbors are sharing your network, specially if you have a wireless network without password.