Hi there! My name is ***** ***** I would be happy to discuss your question with you.
You've got a bit of a difficult question there! E. meningoseptica is a bit of an opportunistic bacteria that is what we call "ubiquitous". That means it can be found everywhere, just even outside in your yard. An opportunistic bacteria is one that you might normally find everywhere, but we tend to see infections develop from it when an immunocompromised animal or person has an "overgrowth" of bacteria (meaning the bacteria aren't fought off as easily due to the immunocompromisation, so they reproduce easier and more than normal).
So my question would be if Hoonah is experiencing an infection from a bacteria that's causing his cough, or does he have something else going on that's causing him to be more prone to developing opportunistic infections.
From a bacterial treatment standpoint, when an infection is not responding to antibiotics, the vets can send a swab to a lab to do what's called a "susceptibility test", which means the test will tell us which antibiotics work best against a particular bacteria. After having run the test, they can prescribe a different antibiotic to help get rid of the current infection. However, if he has something else going on with him that's compromising his immune system, he may continue to get infections over and over again until the issue itself is addressed.
I think your next step would be to talk to your vet about a susceptibility test for this particular infection, then to possibly do some rule-outs for some things that cause immunodeficiency in dogs. One of the characteristics of these issues is continuous infections that don't respond well to antibiotics, which is what sounds like you and Hoonah are struggling with.
There's a link here that gives a nice run-down on immunodeficiency in dogs from the Merck manual.
Does this help to answer some of your questions?