Poor Bridie! unfortunately antibiotics just seem to suppress the symptoms and as you've found out, as soon as you stop them, the symptoms return, and, if the cause isnt due to infection, then antibiotics are no good anyway. Has your vet tested a urine sample? That might give him a better idea of whats going on and then he might have more suggestions for treatment, such as Cystaid or Cystease, both aimed at soothing the lining of the bladder.
What sort of food do you give her? if its only dry food, try giving her more wet food - theres so little moisture in dry food that they rarely are able to drink enough to compensate. Also try her with a pet drinking fountain, might encourage her to drink more - so that the urine isnt so concentrated. Is she an an anxious cat? anxious, nervy cats can be more prone to UTI's - in which case some Feliway plug ins might be helpful.
Just a few suggestions.