What ground does a mother have to terminate the father's parental rights?

I have not seen my five year old son in three years. I moved out of state for two years, and for the past year, I have been trying to visit him. However, his mother has been obstructing visits I've requested. Unfortunately, she was smart enough to say I could visit him in writing, while providing excuses and ignoring requests by phone. Most recently, I asked if I could see him, and she told me that I only could if I signed my parental rights away so that her husband could adopt. I was able to record the conversation and decided that my only course of action would be to file a motion to enforce visitation. She responded to my motion with a petition to terminate my parental rights, likely on grounds of abandonment. I was served during the visitation enforcement hearing, and as a result, the judge decided that she could not make a decision without further research. I am still holding out hope that the judge will order visitation in the interim between hearings, as she said that had the termination petition not been served, she would absolutely grant it. My question is two-fold: Can the judge make a ruling on the visitation enforcement knowing about the impending TPR hearing? Also, can my son's mother claim abandonment when I have paid child support (though I do owe arrears) and have proof that she rebuffed the most recent request for visitation?