I assumed this happens during peak times or in case there are issues with LS. Didn't check the thread FileBeat EOF Error in detail yet but my initial reaction was this sounds very related.
It would strongly discourage to connect filebeat to itself as you could run in an endless loop in case of errors. I would recommend to use a second filebeat instance for this.
I suggest we try to solve this issue here first (FileBeat EOF Error) And then check if the above error disappears?