When Spirit Airlines shut down in May, it left a major void for consumers. Its big yellow planes were gone, and so were the cheap fares that gave millions of travelers a way to fly affordably.Now, all eyes are on America's largest remaining budget airline.It's a carrier that, for years, has shared Spirit's bare-bones business model — and its checkered history of flight delays.But Frontier Airlines' new top executive is betting that, someday soon…