Apparently with the new release of JIRA Cloud some menu items were moved behind "more" button on the issue page & there was a popup about new functionality next to this button which I couldn't close. When I looked in my browser console, I saw:
namespaced-localstorage.js:65 Uncaught QuotaExceededError: Failed to execute 'setItem' on 'Storage': Setting the value of 'grow4316::alexey::more-details-4316-completed' exceeded the quota.
Apparently the application was saving the personalization on the client-side & hitting the limit of the localstorage. Clearing the localstorage saved the day, however I believe such client-side issue could be something hard to track & also frustrating for your users. Latest stable Chrome on OS X El Capitan.
