You could try and proceed and have your parental rights terminated. However, you would need to show one or more of the following, for the Judge to have the ability to do this, assuming it is in the best interest of the child. If it is done, then your obligation to pay support should terminate as well.
Grounds for Termination of Parental Rights
To prove that there are grounds to terminate parental rights, the petitioner must prove any one of the following:
(1) The parent has abused or neglected the juvenile;
(2) The parent has willfully left the juvenile in foster care or placement outside the home for more than twelve months without making reasonable progress to rectify the conditions that led to the removal of the juvenile;
(3) The minor child has been placed in the custody of the department of social services and for six months prior to the filing of the petition, the parent has willfully failed to pay for the support of the juvenile;
(4) One parent has received custody of the minor child and the other parent has failed without justification to pay for the care, support, and education of the juvenile as required by said decree or custody agreement;
(5) The father of the minor child, born out of wedlock, has not made any attempt to establish paternity of the minor child;
(6) The parent is incapable of providing for the care and supervision of the juvenile, and the incapacity will continue fore the foreseeable future;
(7) The parent has willfully abandoned the juvenile for six consecutive months prior to the filing of the petition, or the parent has willfully abandoned an infant for sixty consecutive days prior the filing of the petition;
(8) The parent murdered, attempted to murder, or seriously harmed another child of the parent or another child residing in the home with the minor child;
(9) The parent’s rights have previously been involuntarily terminated and the parent continues to lack the ability or willingness to establish a safe home;
(10) the parent relinquished the juvenile to the department of social services for the purpose of adoption; or
(11) the parent has been convicted of a sexually violent offense that resulted in the conception of parental rights.