The Xbox staying fully (not "funny," right??
) connected for a bit longer is a Red Herring. Ignore it.
First, think of a site that you use often, like say,
www.google.com. The next time everything is up and running fine, open a CMD prompt (Start -> Run, enter "cmd" and then <Enter> key.) Type "tracert
www.google.com" (w/o quote, and entering whatever your oft-used site is instead.) It should display a series of lines showing all the various connections to servers and routers out on the InterWebs, from your router out to the actual site's server. Ignore the gobbledygook that it spews, just check that it completes. That is, that it says "Trace complete." and then comes back to the command prompt. Keep this window around - do not dismiss it.
The next time you have your strange problem, open ANOTHER command prompt and do the same thing again, exactly as you did it the first time. At some point you'll see that the lines are no longer showing "## ms," but instead are showing "*"s and possibly "Request timed out."
You can do this again another time or two for more accuracy if you like. (If you're planning to deal with your ISP, then I STRONGLY advise that you do it another three times in succession, and keep it all on screen, or copy the cmd window contents into a text file.)
Now, examining the list from the top-down, you should be looking at the following (by line # at the far left):
1 is your router
2 is either your modem or your ISP-assigned "gateway" (NOTE: modems will ALWAYS show up as "* * *" here.)
3 and after are "nodes" on the Internet that are handling your connection
The first line that shows all "*"s - that is NOT your modem! - is where the problem is happening.
YOU SHOULD ALWAYS GET AT LEAST THE ISP'S GATEWAY NODE!
* If not, then give this info to your ISP and tell them to get you a RELIABLE GATEWAY within 48 hours or you'll drop them. (Note that you MUST HAVE reliably saved off the data from all the above tests and have it on-hand to show the Tech from the ISP to make this claim stand.)
If the data show that the gateway is responding fine, then the problem is downstream on the Internet, and while likely out of your ISP's hands, worth reporting to them in any event.**
GL!
P.S. If you get no errors, and can isolate YOUR laptop/machine as the source that's "causing the problem," post back here. FYI: I can't imagine that's the case tho....* If you have access to the router's settings, log in to it and look at its "Connection Status" (may have another name) page and copy down the IP addresses given for "Gateway" and both "DNS Server"s. The IP in your router will match one of the first three shown in your "tracert" output.** Story: I once found a problem router that was blocking access to several site/servers for me. (It was physically located in Los Angeles, CA, BTW.) The server was what's called a "backbone" (i.e. "fundamentally important") server, which meant that I was not able to access dozens of sites, as my traffic was (trying to be) routed through that server. But I COULD access other sites that took another route. THIS may be what is happening to you. The Bad News is: ISPs won't do a thing about them, so you're stuck until whomever manages the downed server takes care of the issue.
