Southwest airlines uses an overall cost leadership strategy. this could fail if it:

There are many instances in which the cost leadership strategy could fail with regard to marketing. For one, it could fail if the quality of the airlines suffers because it lowers its cost of operation to give lower fares. Another situation where it could fail would be if it engages in a direct price war with its other competitors wherein Southwest airlines would really have to scrimp their margin down just to compete. Lastly, having too low of a price may cheapen the airlines, depending on what kind of image they would want to project to the market.