Thank you for the detailed description. If I understand correctly, that means somehow Sync is deleting the files on application boot-up (rather than shutdown?) based on the timestamps. If you read the vault folder, right after closing the app, do you see the files disappear, or does it only disappear once the app boots up?
When you boot the app up, and view the sync log, do you see it say “Deleting remote file …” for the files that have been removed?
(Also just following up what WhiteNoise said, any patterns in the file names perhaps, special characters, or maybe just a long directory/file path?)