Due to multiple factors, expect to potentially pay more when booking in May. For low rates, January can be a great choice for travel to Brownsville. Flights to Brownsville from Burbank in January are about $620 on average during January, but can be found for as low as $310.
Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Burbank to Brownsville as you normally would.