I had the same problems,.... couldn't get an IP to stick when the router DHCP doled them out, etc....
The comments about the AC adapter are BS.
What you have to do is update your router firmware. I have a Linksys WRT610N router (Version1), and as soon as I updated the firmware the unit has worked like a charm, and solid as a rock. For the Linksys routers, they have detailed release notes on how to backup your current router configuration, initiating the firmware update (after downloading it of course), and then restoring your saved router configuration settings.
Update your firmware and enjoy your slingbox,... I've hooked my Slingbox Pro HD to my set top box's component video connections and the picture is AWESOME!.