Firewall window pops up then vanishes
I don't recommend Stealth Mode for this reason, constant pop-ups. 

Mac Help says:


  If you don’t either allow or deny access, the message remains
  displayed, and any attempts to connect to the app are denied.


But in  my experience, they dismiss instantly.

Unless you want to manage the firewall with one of the third-party apps--which are certainly available—Apple in their wisdom hath now given us an application firewall, and that's what we've got.