Xbox disconnects when I start an online game the first time

So my problem ever since I've had my xbox 360 is that I keep getting disconnected when i start an online game for the first time. I have tried to look help from here but i didn't see anyone with this kind of a problem. I mostly just play Call of Duty on
online and when I go to search a game I would get disconnected and then I have to connect back and then it would work. This has been for about 6 months and now I'm getting *** about it. I once had the problem where you get disconnected every minute but I got
it fixed hoping it would fix this problem too but it didn't...My NAT type is open and I'm connected through ethernet cable (which works fine). There shouldn't be any problems with my modem. I had xbox 360 slim few years ago and it didn't have this problem.
Now i have Xbox 360 E 250GB if that matters somehow. And sorry for my English, I'm Finnish and this is my first time writing to this page.

Thanks for your help, Beews.

:)

 

Disconnecting pattern

when i first come online and join parties i disconnect after coming back online its fine. after starting a game for the first time after turning on my xbox i disconnect after reconnecting im fine any ideas also my internet is pretty good and im fine on my
laptop and everything i think it may be a console problem

 

whenever i load a game it immediately disconnects me from xbox live.

it also disconnects me when i try to download a patch, after having connected fine when i first start the xbox.