You're welcome to file a bug over at https://tracker.adobe.com/, but this probably has more to do with how the video is encoded (we publish a technical guide on how to best encode video for streaming content providers), or is exposing problems in the video delivery pipeline. It's definitely possible to deliver video reliably using Flash Player when filing the guidelines, but the video codec standards themselves are super broad, and there are a lot of buggy encoders in the world. Not all choices in that world are good ones.
If you do decide to report that bug, please include details about your platform, like the browser and OS versions, whether they're 32 or 64-bit, etc.
For Firefox, I would try disabling hardware acceleration in Flash Player as a workaround. Our software video decoder is more CPU intensive, but also much more forgiving than a hardware decoder.
Most of the US browsers are well along the path of removing support for Flash Player. I have to imagine that this issue is very low priority for them. The recommendation would probably be to contact the content provider and encourage them to migrate to an HTML5 video solution.