Airlines that have been closed by the user or by the automation (bankruptcy, not enough credits, inactivity etc) can not be restored unfortunately. Since the airplanes and slots may already have new owners and so forth.
According to the game logs the warning of inactivity was sent to your email on May 21st, and the airline closure happened on 27th. The warning resets by logging in to the site, and visiting the dashboard (or any other sub-page) of that particular game world.
If you are absent for a longer time you can use the holiday mode (from dashboard->settings) to prevent the inactivity checker/closure.