Whenever I try to play a game online I am usually unable to find a game and if I do manage to get into a game I am disconnected from xbox live soon after, however after I sign in again the problem seems to disappear.
I'd start by clearing the system cache (it's just updates plus other temporary files, nothing that's at all important to anyone) by:
1) Tap the silver Xbox Guide button on the controller, go right 2 clicks to Settings, pick System Settings.
2) Select Storage (or Memory).
3) Move over any hard drive or memory unit (not the Cloud) & press (Y) on your controller & pick Clear System Cache.
4) When asked to confirm storage device maintenance, choose Yes.
Some NAT problems are subtle and don't appear in the Test Xbox Live Connection test. Most likely there's a port blocked... ports can be blocked in your router,
modem, or at your ISP. Since the Xbox 360 uses different ports than PCs & Macs use, you can't see the effect of a port blockage
except on the Xbox.
A sequential power cycle is the first step in clearing a port blockage:
1) turn off the Xbox then
2) unplug the power from the router (Some folks have a combination modem-router AKA 'gateway'. If so, skip step 3).
3) unplug the power from the modem.
4) Wait at least 30 secs then replug the modem (or gateway) power.
5) Wait 'til the light on the front of the modem (or gateway) which says ONLINE, READY, CABLE or DSL is on solid (not flashing), then plug in the router. If you have a gateway instead of a modem and router, then when that light says it's ready, skip step 6.
6) Wait until the WiFi light on the router is on; you may not use WiFi, but it's still a good indicator your router is finished booting up.
7) Turn on the Xbox. For more background on Ports, see
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