I was diagnosed with BV several years ago and it would not go away. First we tried switching to a different antibiotic but that did not work. Then I was put on a very low dose antibiotic for a very long time (I do not remember what it was and unfortunately don't remember how long I was on it but I think it was 3 months). It finally went away. I know that seems like a terribly long time to be on antibiotics but it was a very low dose. I will try to see if I can find what it was in my records but not sure I will be able to as it was a long time ago. Just thought I would mention this because sometimes they pick a broad spectrum antibiotic which may not be best to target what you have. If you have been repeatedly put on the same antibiotic you might ask your doctor about changing it up.
I am so sorry you have to deal with this and I recall how frustrated I was. It was actually my urologist who suggested the low dose antibiotic as I recall. Please keep us posted on how you are doing.