That means you are using the ‘local’ web app, which is almost always a bit behind of the ‘hosted’ web app.
Please compare the behaviour of the hosted web app at https://app.plex.tv/desktop
It looks like there is everything in order with the subtitle file.
When this happens, can you determine whether the subtitles get ‘burned in’ by the transcoder or whether they are rendered by the browser on top of the video picture?
You should be able to see this by looking at ‘Now Playing’.
If it says ‘Direct Play’ for the whole file
or ‘Direct Stream’ for the video stream, then it is the browser which loses the subtitles.
If it says ‘transcoding’ then it is the transcoder which loses the subtitles.
So it is more likely the client, which loses the subtitle.
Could you enable debug logging in both the Plex web app and the Plex server and fetch log files from both a few seconds after it happens to you again?