If this is happening, then I can't imagine it's a hidden feature, but more likely a bug. I haven't seen anything on the known/resolved issues list that refers to this issue, so suggest you raise this directly with Tableau Support as it is a significant issue.
Before doing this though, can you guarantee someone else hasn't got the rights to amend project permissions? Also I'm not familiar with how an HA environment works when it comes to user/content/permission mangement, but is there a chance something isn't getting properly replicated around all the servers?
Sorry - no answers, but hopefully some ideas to think about!
You could check in the repositry (Historical Events), as to whether there were any updates to the project (and when and who did them)
It wont tell you what the update was, but at least will tell you if anything has happened to that project
Hope this helps