Great connection, frequent disconnects

I'm by no means a network or connection expert but I see no one has answered you yet.

I can tell you that it doesn't appear that it is a problem with your U/L and D/L speed as those are adequate.  

I have seen and heard about this issue pertaining specifically to the "Custom Game" modes and affecting quite a few people which makes me wonder if it has to do more with inadequate internet speeds or NAT issues with the individual hosting the custom game.

What do you think, could this have anything to do with the issue?

Thank you Knowitall, I kept trying to respond but could not get the reply box to appear in firefox so I switched to IE after seeing your reply.  I too agree that the host or other members of the custom game could have a NAT that is not open or could have a very poor connection causing the issue.

Thanks for the replies.  What I don't understand is, why they can go about hosting custom games with the general public (meaning lots of non-friends joining) with no problem, but I specifically cannot connect to them every time.  To me, that seems to indicate the problem is likely on my side, but of course I base that on absolutely nothing :).  When I am not using a router, can their NAT settings affect my ability to connect?

Yes, it all has to do with how the packets of information is routed into the person hosting.  Distance also plays a part.  There are many things to consider but I know Reach has some networking reports you may check in one of the menu options.

Some updated information...

I tested with a friend's Reach disc, but the error still occurred.  I tested with a friend's Xbox 360 (a newer one w HDMI port), but the error still occurred.  All the while, I was playing with my Xbox directly connected to the cable modem.  Each test, I got disconnected from Xbox live after about 5 games.  When the disconnections happened, my entire internet connection would go down, meaning I'd have to reboot the cable modem.

As I mentioned in the OP, the in-game network checks in Halo Reach all indicate optimal status (green), including the NAT indicator which reads 'Open'.

Sorry, I don't mean to second-guess your answers, but everything I have read indicates that NAT settings only apply to router usage.  If I am not using a router, isn't that the equivalent of an open NAT?  I don't understand how the host NAT settings (which I confirmed to be Open by the way) could affect me in this case.

Anyway, basically the only thing I can think of to try that I haven't already, is using a different cable modem.  I am reluctant to buy one however because the problems seem limited to Halo Reach custom games.

If the disconnect takes down your entire network, then it sounds like your modem is faulty based on your statement above.  I'm not sure why you see it mostly with Reach unless the amount of traffic is overwhelming the modem to the point of it hanging.  I'm not sure how easy it is to replace your cable modem as your ISP authenticates with the modem's MAC address if I remember correctly but it seems the likely source of your problems.  

That brand of modem is outdated by four years (atleast it is through TWC). I used to have the same one though Time Warner Cable until February of this year. They replaced it for free with a smaller newer modem. I would check with your cable provider and see if they have a new modem available for trade in especially if you have had yours for more than a few years.

It definitely sounds like an issue with your modem. Everything else you have listed seems to be in order.