Alright, this is a weird (as far as I understand it) problem. I haven't found any other solutions to this problem and have no idea what to do now.
Here it goes:
A while back I bought a Wireless N Adapter for my Xbox 360. (This is one of the older consoles too, not one of those new "Xbox 360 Slims.") It never worked, so I honestly just rat-holed it away out of frustration.
Recently (because I've become more efficient / knowledgeable with computers and internet connectivity etc. I decided to give the wireless adapter another chance.
I read online that Xbox Live requires a certain MTU setting of around 1364 (or something like that) or higher. My MTU setting is at 1500, well above the 1364 (or whatever it is) minimum. However, despite my wireless internet router being at that setting, the Xbox still reported that there is an error with my MTU setting.
I was continually being disconnected from Xbox Live while using the wireless adapter; however, I began checking to see in my wireless internet router was the cause of this problem.
It turns out that there is a slight problem with Xbox Live and my router. However, I read online that opening up ports (through port repeating / port forwarding) associated with your Xbox's internet connection could solve this problem. So I began opening ports 88 and 3074 (which were the only two displayed on my router's manufacturer's web support guide.
Everything was working excellently... for a while.
Now my Xbox will connect to Xbox Live properly (not log me out every 5 minutes) and I can chat with friends in parties and play games online. However, rather than being disconnected from Xbox Live completely, I'm (seemingly) locked out of only some parts of Xbox Live.
For example, I was just in a party communicating with my friends (talking, joking, etc.) and I tried to join a game of Tom Clancy's Ghost Recon Future Soldier online multiplayer. However, as soon as I pressed the start button, the game came back with the message that it could not load the online servers (they were "unavailable at this time"). I associate this with an "improper" or "inadequate" connection to Xbox Live. What I mean to say here is that I can talk with friends in parties but can't play online. Also, the same goes for Gears of War 3 when I try to get into online games of Hoarde or any other online mode. The Xbox will search for matches, but it just won't find them; then, I'll go to the Gears of War 3 main menu and look at the "Events" section and it will state: "Cannot access the Gears of War 3 servers at this time." (Or something to the same effect.)
I forgot to mention that when the above occurs it will be "bipolar." What I mean by that is that when I first start up my Xbox, I'll find games with ease. Hoarde and Future Soldier multiplayer will do fine, but when I switch games, it will refuse to connect me.
What I do afterwards is check my connection to Xbox Live under the Settings - System Settings - Network Settings area of the dashboard. When I use the "Check my connection to Xbox Live" option it no longer states that I have an MTU error, it now states that I'm not even connected to the internet. The problem with this is that right before I do this check, I'm in a party talking to friends with no interruptions, no lag, no static, no interference whatsoever. (In other words, I know for a fact that I am connected to the internet... you have to be in order to use party chat.)
I know this is a long and drawn out "story" however, it's just been a real big disappointment. In short, all of my wireless internet router settings are fine, I've opened all of the necessary ports for my router to function better with live (I should also mention that I've opened all 4 Xbox.com suggested ports as of now - Ports: 88, 3074, 53, and 80.) It's just my Xbox gets... "confused" and just doesn't understand / isn't consistent in its detection of whether or not it's connected to the internet. (Again, I know for a fact it's connected because I can communicate with my friends, but while doing the "Check my connection to Xbox Live" it states that it's not connected to the internet at all.
Thank you for reading this far. And I appreciate any and all help.