Patents on antibiotics last no longer than on any other type of medicine (20 years, minus the substantial time taken to test it, jump through regulatory hoops, and bring it to market -- typically 8-14 years). The cost of meeting those regulatory prerequisites is measured in the hundreds of millions of dollars in the USA alone -- more if you want to get a product license everywhere worldwide. So you need to earn back several hundred million bucks in profit in a single-digit period of years ...
But antibiotics are unprofitable. A typical AB course lasts 5-14 days after which the patient is completely cured. Compare with antidepressants or ADHD drugs -- where you get a customer for life! Which would you invest in, if you were in that business -- a product 10% of the population will use annually for a week, or a product 10% of the population will be hooked on for life?
It's not a coincidence that research into new antibiotics ground to a halt in the 1970s around the time that the regulatory barriers to entry rose so high that small and medium scale pharmaceutical companies were frozen out of the business and the surviving operators were the large conglomerates.
(Disclaimer: wearing my ex-pharmacist hat here.)