Videos on Facebook will not play in Safari on Mac but will play in iOS

I've been finding recently that, consistently, live videos I have put on Facebook, while they have been accessible on Safari on the Mac when they are live, afterwards cannot be played. They are replaced with a black window with a rotating blue circle. I have tested this on several MacBooks and iMacs, running different MacOS version up to Big Sur, and they are all the same. There is no problem with the same videos on iOS devices. Also there are no problems on these Macs with videos on other sites: it is only Facebook that is the problem, and I've only seen the problem with the videos I have recorded myself, using OBS (Mac) in conjunction with Facebook Live Producer, not with anyone else's Facebook videos. And nobody not using a Mac has reported any problem with my videos to me.

Has anybody got any idea what is going on?