Mediation is a voluntary process.
Unlike arbitration, which is imposes participation requirements, in mediation, parties who do not like the way things are going can walk out. The real issue for the mediator is to find out whether a party who walks out is quitting the process or undertaking a strategic or tactical move. You may conclude you should follow the person out of the room to find out what is going on. On the other hand, it might make sense to wait several hours or even a day or two to give that person a chance to cool off. A mediator needs to meet with the 'opposing' parties separately before the process begins as well as during the mediation.