How could they lose money relative to Southwest? Frontier's fares are higher, they charge bag fees, they charge change fees and they charge for Direct TV, or they charge for Classic or Classic Plus, which are even higher than Southwest most times. They fly to cities (like Akron, Fairbanks, Anchorage and several in Mexico) that Southwest won't go to, so they have a captive market for those and can charge even more. When Southwest enters a market they are in, they pull back service.
Could it be that when given the choice between higher fares and lower fares, people actually will go with the airline that has lower fares? Could people actually be smart enough to factor in bag fees and change fees in their purchasing decisions?