Hello,
the Web Player (Firefox or Chrome it doesn't matter) will almost always stop playing an episode before the episode ends.
Will use specific latest episode I saw with logs to discuss behaviour:
a) The episode is identified well for duration, showing. Full episode is 21 minutes, player stopped at 19 minutes. The time was 15:15 local.
b) When it stops playing, the screen is the series background with an active play button in the center of the screen, the timeline below still showing 19:01 and the timeline is filled up to the point of that time, so orange until 19:01.
c) Pressing play button in the screen does not have any other effect other than making all the timeline grey again, but it just sits there attempting to load, but does not. Button pressed at 15:23 (around, did not clock this correctly, apologies). At 15:24 (late minute) I pressed pause next to the timeline to stop it trying to playback. Screen is back to what it was, the series background with a big play button in the center.
d) The URL to access Plex server through my internal network is http://192.168.1.253:32400/web/index.html#!/server/ [and more identifiers]
e) The Plex Server is latest version, no upgrades detected bia the check function.
f) The Plex Server is on a Windows Server 2008 R2
g) The browser I use is running off Windows 10, with no outstanding updates.
h) The browsers (Chrome and Firefox) are both updated to latest, verified today as well.
i) the home network is 1Gbps.
Logs attached, which were set to debug and verbose.