How to keep user signed in?

I have a set of large screens shown to operations team which keeps asking for credentials when network goes down. Is there a way to (safely) persist credentials so it wont ask over and over?

Are you using just the Basic Authentication that Shield gives, and logging in with the Shield UI login screen? If so, then as long as the browser is sending valid cookies your session should continue working.

You might be getting hit by sessionTimeout which is 30 minutes by default. You can try making that longer.
https://www.elastic.co/guide/en/shield/current/kibana.html#shield-ui-settings

Another more drastic option would be to disable Shield UI (the method of doing that depends on which version of Kibana you are using) so that the session uses just HTTP Basic authentication. That would make your setup so it isn't cookie based. By doing that, you will only be able to log out by quitting the browser.