There is no definitive answer to this question as it depends on so many variables such as the nature of your condition, your overall health, how long you have had this particular condition, your response to acupuncture treatment and, indeed, the skill and experience of your chosen practitioner.
As once-off miracle cures are still rare, you should commit yourself to a course of treatment and be prepared to give it a chance. Usually, if your condition is going to respond, then you can expect to see results after about 4-6 treatments. Acupuncture treatments seem to have a cumulative effect with each treatment building in the effects of the previous treatments. It is thus not unusual to see little or no improvement after the earlier treatments but to suddenly experience an improvement in your condition after about the 7th or 8th treatments as if you had passed some kind of threshold. This is why it is important to commit to a course of treatments. However, if you are experiencing no improvement after about 10-12 treatments, then you may be one of those people whose condition is not amenable to acupuncture. At this point you should discuss this with your practitioner and re-evaluate acupuncture as a treatment for your particular condition. Your practitioner may be able to refer you to another complementary medicine practitioner who has had success with conditions similar to yours.
It is important to note that if acupuncture didn’t work for you then that is not to say that acupuncture will not work for somebody else with a condition such as yours, as Acupuncturists treat people on a holistic basis, just because your migraine condition did not respond is not an indication that somebody else’s migraine condition will not respond, everybody responds on an individual basis.