Depending on flight schedules, Spirit Airlines' counters at DTW have different hours of operation. The counters typically open three hours prior to the day's first scheduled departure and close after the final flight leaves. If you require specific office hours, it is recommended that you check online or give us a call in advance. international Spirit Airlines Detroit Office choices in Latin America and the Caribbean. The first thing to do if you miss your flight is to go to the Spirit Airlines customer care counter at DTW and check whether there are any options for rebooking. Subject to seat availability, Spirit Airlines' "Missed Flight" policy may allow you to board the subsequent flight for a charge. Since other planes can fill up, it's critical to move fast.