Does a custody mediation expire if one of the parents is not abiding by agreement? Is a custody mediation legally binding?

Upon the completion of mediation, if there is an open family law case then the mediator will file the outcome of mediaiton, including any agreements with the Court.  If there was mediation in contemplation of possible litigation then the Court would not have approved the agreement.  If both parties sign an agreement, then it is arguably a breach by one party for not complying with the contract, but if there is a court case and the mediated agreement has been approved by the court then it becomes an order of the Court and non-compliance can be considered contempt.  The only means by which to modify a mediated agreement is for the parties to come to another agreement.  The mediated agreement for which you have entered into at this time does not expire, once you sign the agreement, it is essentially a contract.