Can the non custodial parent take full custody away from the other parent if he has demonstrated an 'on again- off again' style of parenting?

To give a lawyer's answer...It depends. It depends on a large number of factors, the jurisdiction the court which has authority of the case, and the particulars of the "on again, off again" partent. In any event, it will require you to hire a lawyer and he will have to go to court and argue that the other parent is an unfit parent. One thing you must realize is that even though the law is gender neutral, most courts strongly favor the mother. * Only the court has the power to award or rescind custody. The court of jurisdiction in custodial cases is the one that issued the original order. The exception being if there is substantiated and indisputable evidence as defined by existing state law that the presiding judge 'grievously erred" when he or she rendered the decision. A major factor in all custodial cases is the parenting plan that each parent is required to submit to the court, rather than the attempt to prove the other parent to be unfit. It is difficult to ascertain what the term "off and on again" means, when it pertains to a parent who has been awarded full custody. Full custody indicates that the named parent has the children in their care, or in the in the care of a qualified adult/caregiver, except for required visitation by the non custodial parent. Full custodial rights further dictate that said parent has the legal power to make all decisions concerning the welfare of the child or children (education, medical issues, etc.) Be that as it may, no person (including an attorney) can guarantee the outcome of a custodial case (or any case for that matter).