I stream a lot of TV on my computer too so I can understand how frustrating it is to experience this issue, all of a sudden. Has this worked for you in the past and only recently stopped or is this the first time you are attempting to access it?
I have attempted to access it on my end and it worked without issue. Please visit https://go.cnn.com and then you'll need to sign in to view live TV. There should be an option to sign in on the top right corner of the screen, you'll need to select your provider from the list. It is easier to simply search for "Rogers" in the search bar that is available. Sign in using your MyRogers Profile login and you should be able to stream CNN's Live TV Feed.