This issue was reported in May 2019 and it got no responses. So I am going to try.
Videos viewed on YouTube and other sites will only pause momentarily (maybe 20 seconds) and will then begin playing again. I am using the default Brave settings and this happens with both shields up or down.
The site works as expected using Mozilla or Chrome. I’ve noticed this on www.youtube.com, and just about any site that streams video.
Brave Version 1.24.86 Chromium: 90.0.4430.212 (Official Build) (64-bit)
Microsoft Windows Version 10.0.19042.985