For as long as I can remember, there has been an issue with the web player in that if you pause the player and then try to resume a little later (without testing, this can happen after 10 or 15 minutes of being on pause, possibly less), the player will only play as far as it has buffered and then fail.
I haven’t tried this for playing media on the same network, only for remote content. It’s definitely not a bandwidth issue.
I’m using Safari on Mac OS Mojave and previous versions of Mac OS.
Server Version#: 1.16.3.1402