While some Lyme-literate doctors are probably more adept at treating Lyme than others, it may not be a good idea to fire your doctor, just because you aren't improving much on your current treatment regimen. Because the doctor may not be the reason why your progress is slow.
Healing from Lyme disease is very much a patient participation thing. Doctors can't carry the responsibility for your wellness; you must help them. In a big way. Because they may know the proper medication for Borrelia, but they might not know how to balance your hormones, (in which case, you also need to enlist the help of an endocrinologist or naturopath, since balancing the hormones is an integral part of healing).
Also, if you aren't completely following their protocol for you, this may impede your progress. Yes, sometimes our intuition is better than the doctor's recommendations, but not always. For instance, if your doctor tells you to avoid bread and pasta in your diet, and you don't do this, then you may not heal, no matter which doctor you see.
In addition, if you are really sick from Lyme disease, you may not see improvements in your symptoms for a long, long time. Little positive changes may emerge, but major changes in your well-being may not happen for a year or two. The healing process is extremely slow for the really sick and winning the game requires a hefty dose of perseverence. Don't switch your doctor because you aren't running around on a playground after six months of treatment. I have known people who have been on antibiotics for five to seven years, and who are now mostly well. I doubt they felt stellar after the first year on a regimen. But they hung in there and reaped the rewards. Personally, I don't think that I could do a regimen for a couple of years without seeing major results. I am too impatient, but I do believe that's necessary to stick with any protocol for at least six months to a year to know whether it's even going to work for you.
In your desperation, you may want to run to the next thing or the next doctor, but think carefully before you do Yes, I know people who stay on regimens for years with little progress, and I believe that this is just as unwise as jumping from treatment to treatment every few months, but more often, people don't give their current protocol a chance.
Finally, treatment failure may not be due to the fact that your doctor is incompetent. It may be that your case is complicated, and that you are a challenge, even for the best of the best. But don't despair--if this is the case, try to work with your doctor to discover what might be blocking you in your healing (if he or she is willing to explore the possibilities), and if you are unable, only then may you want to consider moving on to a different health care provider or treatment regimen.