Broken relationships can have a dramatic effect on the children more than the anyone else. This type of situation is the very important reason, in my opinion, why it is vitally important for the biological parent to be held accountable for their portion of the child / children's financial well being.
Now, on the flip side of this: Yes, he can be held responsible:
There has been court rulings on just this situation under the
Child Support Enforcement Amendments of 1984, P.L. 98-378, Section 18 as codified at 42 U.S.C. sec. 667. The state cognate is Chapter 460 of the Acts of 1993.
although I am sure there must be a certain time frame set to argue this motion. JudyKayTee can probably lend a better insight to that aspect.