Why do antibiotics not work well against pseudomonas aeruginosa?

Various reasons: Pseudomonas is a very common bacteria which has developed many clever ways of resisting different antibiotics. It can destroy the antibiotics with chemicals, pump the antibiotics out of its cell or become 'invisible' to antibiotics by changing the appearance of the bacteria. Pseudomonas can adapt to antibiotics & change during the course of treatment. Serious infections often require an expert.

Antibiotics: Pseudomonas is a gram negative rod bacteria that lives in soil and water. Although it is true that pseudomonas is resistant to many antibiotics, there are quite a few that, when given iv, are effective against this bacteria. The resistance is due to the mechanism of metabolism that has evolved to "inactivate" less powerful antibiotics and oral antibiotics.