P. aeruginosa is an incredible organism. Not only is it antibiotic resistant, but it also is starvation resistant. So even when you have antibotics that work, it's often to difficult to get them to all the cells, since cells at the bottom of a biofilm just shut down completely for weeks on end. End the course of antibiotics, and they pop back up and start growing again.

Thankfully, there are major tradeoffs associated with those traits, which makes them not particularly virulent to healthy people.