it's not just CNN, but a bug affecting many websites, Netflix, Amazon Prime, some of the major broadcast networks, which no longer us to see any of their videos, shows, movies, etc
Can't make any confirmation of the streaming vendors you mention. We only have a TiVo in our home to record and watch OTA programming. Well, not entirely. We can watch Amazon (non Prime) movies and quite a few other services that can be linked through it. But that's not a PC or Mac, so the issue isn't really the same.
For us, on either of our Macs or iPads, CNN in Safari, only on the Macs, is the only news site we've tried where videos stop at a random point and turns black. No problems at all when visiting the site with Firefox, or using Safari on an iPad.
CNN has their own page for "fixes" with Safari and other browsers experiencing video playback issues. Tried them. They don't work.