looking for the same thing!
i, my husband, and our kids all live in southern tx. i have been up and down the web trying to find a law that states at what age can a child decide whether or not continue visitation with non-custodial parent. my husband has joimt managing conservatorship with him being the custodial parent. his children do not wish to visit their mother any longer who abandoned them when they were little.
i believe they love her, but they realize that she only saw them when it was convenient for her. my husband and i do not attempt to persuade the children one way or the other. this is something that they have expressed.
from what i read, i have gathered that there is not an age when children can actually "decide" if they want to continue visiting the other parent. do not quote me and please double check, but i am pretty sure that i understood the law to state that there has to be a "change in circumstances" in order for the cp to file for mod. of visitation or seek sole custody. when a child has expressed desire as to which parent they wish to reside with, the court(judge) will take the child's wishes into consideration upon making a decision. it is ultimately the judge's decision to grant this order however.
the law repeats itself in using the ultimate tool in a judges decision: 'BEST INTEREST OF THE CHILD"
with saying that, i will tell you that i am brand new to this whole custody battle situation, and right now i do not know which end is up. i would suggest discussing with your child the reasons as to why he/she wishes to discontinue visitation. obviously, if there is abuse or exposure to danger, then i would definitely consult a lawyer and get the ball rolling. it could simply be that he/she is bored at the other parent's home and doesn't want to go. maybe there is a problem with other siblings in the home. if it is a minor issue, and you have decent communication with the other parent, it might be wise to consult them first and try to explain the situation before dragging it into court--WHERE IT IS COSTLY TO IRON OUT DIFFERENCES
good luck and i hope this rambling offers you some decent advice