The short answer is yes, but there are a lot of ifs ands and buts to this topic. Every family situation is unique. The first factor is the age of the child.
If children are younger than 16, the custodial parent should do everything possible to keep the children going to the possessory parent for visitation, with some caveats. Obviously, the custodial parent needs to recognize when the children seem afraid or have other changes in their mood and personality. This could but may not signal that something is wrong. If you suspect child abuse you should immediately take the child to Dell Children’s Hospital for evaluation. Sometimes when a new person comes into the other parent’s life the dynamics between the child and the parent change. They may give the child less attention or one-on-one time. Or they may abdicate their parental responsibilities to the new person. There also may be additional children in the mix from this new person.
If the children are 16 and above, there are a lot of different factors in why the children don’t want to continue to visit the other parent. The biggest reason is that kids that age may be driving and they have more freedom. At this time in their lives they are pulling away and/or rebelling. It is a normal phase that has to be lived through. If the children don’t have a good relationship with the other parent, it isn’t going to help the situation by getting into battles with a teen.