Who is good in law?

Jessica
My child's father did not sign the birth certificate in the hospital because he did not have any form of ID with him. He was there for the 1st year of her life. When I decided that I didn't want to be with him, he slowly stopped coming around. He went from seeing for every day, to every week, every other week, etc. My house is always welcome to him. We do not have any problems with each other. I tried to invite him over and he accepts, but of course never shows up. It has been a full year since he has seen his child or helped out in any way with her. No phone calls, texts, nothing to assure her well-being. 
I want to know how long does he not have to be in his child's life before he loses his parental rights?