I watch it also but am restricted about naming the service here. But it does work fine.
I watch it on USTVNow.
Yeah, I've tried that svc, too. I'm just not big on having to have my computer running in order to watch television. My little pet peeve, lol.
The only legal way of doing it that I know of is USTVNOW. JustIn TV feeds are pirate feeds that get pulled down regularly by Justin TV.
I used to watch it this way, too, and you're right they're pulled constantly. I wonder if the OP is trying to access an old one? It helps to enter CNN in the search to get the latest.
Also, doesn't CNN (US) show in the evening on CNN International? Someone here hipped me to that when I first cut the cord. Helped with my CNN fix until I found alternatives.