Quick navigation does not drop down from quick search for anonymous users

Symptoms

When not logged in, if you type something in the quick search bar, it looks like it's loading the quick navigation, but then nothing appears.

Steps to Reproduce

1. Access a site with anonymous access, without being logged in
2. Type something in the Quick Search bar

This is reproducible on confluence.atlassian.com at the time of this writing.

Workaround

If you hit enter, then the search will still be performed.