Hello, this is Dr. Bruce and I would like to help you with Bob.
I'm sorry to hear that he is having this problem.
You don't say how long this has been going on for, or what form the antibiotics were given (drops in the ears, or by mouth). I am assuming that he has a chronic ear infection, thus the head shaking and the balance problems.
Whenever I deal with an ear or ears that have been infected and are not getting better, it becomes important to determine what specific bacteria are growing in the ear, and what antibiotics will be effective. Over time, the bacteria in the ears can mutate and become resistant to some antibiotics.
I would strongly suggest having your vet send out a culture and sensitivity of the ear discharge. This is a test where the vet takes a swab of the ear and sends it to a microbiology laboratory. At the lab, they will grow out the sample, and determine what specific bacteria is growing in the ear, AND what specific antibiotics will be effective against that bacteria.
By doing this test, you will be able to provide Bob with a more targeted treatment and give him a better chance to heal.
After the results come back, your vet will be able to provide the correct treatment. It may be necessary for a medication to be compounded to provide the correct antibiotic for the ears.
I hope this helps and that Bob is feeling better very soon. If you would like to continue this chat, please reply to this post and I will get back to you as soon as possible.