CiviEvent 4.7.7 Issue with Repeating Event
Unfortunately I wasn't able to recreate this error on the demo site (4.7.8), or on our installation. I also couldn't see an issue related to this in JIRA.

It looks like the JavaScript that conditionally displays those settings fields isn't working correctly on your site. You could check your JavaScript errors console to see if any problems are coming up.

Eg: in Chrome, press F12, go to the 'console' and then reload the settings page and try to make your changes.