The situation you describe is rather unusual, not in that you each had persistently positive tests following treatment but that it has taken so long for your BF. the nature of most chlamydia tests currently used (PCR, ProbeTec, Aptima) is that they do not detect living organisms but there DNA. The DNA can hang around following effective treatment for a number of weeks, leading to repeat positive. In addition, while rare, there are occasional false positive tests.
The effectiveness of both azithromycin as a single dose and doxycycline take for 7 or more days exceeds 97%. For those rare treatment failures, re-treatment with either the same medication or the alternative is almost always effective.
My advice, given your abstinence since diagnosis and repeated treatment of your BF, I would be quite surprised if he (or you) were still infected and would look for an alternate explanation. Retesting with an alternate test or, even better, a culture would be an appropriate next step. Hope this helps. EWH
I guess one thing worth mentioning is that he does start to feel better when he takes the antibiotics but when he's done with them the symptoms come back.