You may have a problem with your router or cable modem if your Roku player is disconnected from the Internet long before the four-hour limit is up; however, please remember it is supposed to disconnect after that time limit expires. To watch longer than that, you have no choice but to click "yes" when the window pops up asking if you want to stay connected. I live in northeastern Ohio, have had a Roku player almost a year, and have had no problems at all in this regard, but then again I rarely, if ever, watch more than two hours or so of live television at a stretch.
Please remember as well that the Roku player does not operate the same way regular over-the-air television does. Due to the Internet being a shared resource, the Roku cannot remain connected forever; this is why the warning window appears after four hours, with the option to reconnect if the user desires. If you want TV with no limits at all on viewing time, I suggest you get an antenna and connect it to your television. There are no time limits on viewing with an antenna.
There is no way to legally bypass or circumvent the four-hour timer on Roku players. As I said, if you don't want to be interrupted by warning windows asking if you still want to watch a given channel, forget the Roku and either get cable or a television aerial. Then you will be able to watch television to your heart's content without any interruptions whatsoever. There are Internet web sites that show warnings as well if you remain connected to them too long; Radio-Locator dot com is one of them. This site warns anyone who remains connected more than a certain short period of time that they have exceeded their allotted time and/or bandwidth limit and will be disconnected from the site shortly.
The reason for these time limits is, as I said, that the Internet is not the sole property of any one person or group of people, but is a shared resource; there is only a certain amount of bandwidth available for the shared use of millions of people worldwide. There is, and never has been, any tolerance for bandwidth "hogs" or for anyone who remains connected to one web service, including streaming video, for a ridiculous length of time. I have never heard of anyone being banned from the Internet for bandwidth hogging, but that doesn't mean by a long shot that such bans have never been imposed. I am sure there may have been isolated (or not so isolated) cases of people with a history of habitually hogging certain websites being told not to use them again; I likewise have never heard of anyone being banned from the entire Internet for these reasons, but again, that does not necessarily or in fact mean such action will not be taken against bandwidth hogs if necessary.