How long before the non-custodial parent loses parental rights after abandoning his children?

I have a problem with my ex-husband who is not paying any child support, is over $7600 in arrearages, has moved to another state, and ignores his kids' birthdays, special dates, and hasn't seen his children since beginning of the year. I am struggling to provide for them and I can't afford an attorney for advice, but needs to know on what grounds I could possibly petition for his parental rights to be dissolved. I have been with my fiance for over a year, and he is more than willing to adopt them if my ex didn't have parental rights. In my opinion he shouldn't, given the abandonment and non-payment of support.