A couple of things to try.
First: Reboot your modem (not your router). Just unplug your modem for about 15 seconds and plug it back in. Give it a few minutes just to make sure it's fully booted back up. If that doesn't work, see second suggestion....
Quick question. Do you have a wireless access point or do you have a router with 4 ports (5 ports including the "Internet" port? A wireless access point will just have the one "internet" port and no other ports.
Second: If you have a router, hardwire your XBOX directly to your router. If it works, then that means that your wireless settings are messed up somewhere. If hardwiring into your router doesn't work, then hardwire directly into your modem. If that works, then that eliminates your modem as the problem. Then that would obviously be your router as the cause of the problem It could be a setting or it truly is going bad (although not likely).
Troubleshooting/Process of Elimination is the first and most important step. Once you figure out the problem, then worry about resolving said issue.