I remarried my ex-wife 1 month ago after divorcing in 2005. She is an alcoholic, who had since been through treatment. She is now drinking again and I do not want to remain in the marriage. Do I need to get another divorce or am I eligible for an annulment, due to fraud (resuming drinking)?
You may be able to obtain either an agreed annulment (invalidity) or an agreed divorce if she is in agreement and as allowed by the laws of your state. Assuming that she is not in agreement, the grounds for a finding of an invalidity of a marriage vary from state to state. The more common grounds for annulment are that the party was legally impaired at the time of the marriage, such that the decision to marry was not freely made, or that the other party fraudulently represented their status as to the applicable “essentials” of the particular marriage, such as being of legal age, being unmarried at the time, being able to conceive children, or being of a particular faith. Promises to behave in a certain manner or to not engage in certain conduct (such as drinking), even if explicitly made in writing or as part of the ceremonial wedding vows, would normally not allow for an annulment based upon failure to abide by those representations.
Your question indicates that you were aware of her treatment status and that she did not conceal her treatment status at the time of the marriage, but that she has since relapsed into drinking. Under traditional general concepts of fraud, her conduct at the time of the marriage was not fraudulent, as her then-current status was apparently fully disclosed. Her later relapse, while unfortunate, does not change that her status at the time of the marriage was fully known.
Unless there are critical property or other issues that would be protected by an annulment but not by a divorce, which are not included in your question, it would appear the simplest approach would be to pursue a divorce as the legal results should be the same as an annulment without the additional legal issues outlined above.