Ray Darr,
Try turning off any Encryption and Passwords. Just have it log on normally. If you want you could set the MAC Address of your Wireless Card to be the only one allowed to log into your Router.
See if it still loses the signal then.
It would help to know the specs on the comp you are trying to connect, including the OS you are using.
Take Care,
Richard
P.S. What happens if you just tell the comp to reconnect to the wireless connection instead of resetting the Router?