Is there a limitation on the non-custodial parent's rights if s/he is not in contact with his/her child?

Each parent has the same equal rights to a child and to see a child unless those rights are limited by agreement or court order.  What does your custody and visitation order state?  If you wish to modify the order or agreement you are going to have to either get consent or a judge to do so.  I understand you are upset about their not seeing the child but this does not limit their rights automatically.  Good luck.