I don't mean the "Repair" button. I mean simply starting the launcher and looking if a popup already appears.
Well, the message about an "ss9" mirror looks so hopelessly outdated... from this state, the launcher is probably not anymore able to upgrade to version 0.5.8; better re-install the game with a current installer package. Doctoring the config files in the game installation directory or in your user application data directory may or may not help, even completely mess it.