As Andrew Paton has observed: “Mediation can never proceed faster than the pace of the slowest party”.
It’s not all that unusual for a party to come under-prepared and to use the mediation day to work out its risks and therefore its negotiating position. This can be frustrating for others who are well prepared and ready to negotiate.
It’s important to set one’s clients’ expectations in advance. Perhaps suggest they bring other work to fill the down time or even a good book.
A good mediator should be able to help the laggards along and minimise delay, but there is a limit to what he/she can do without becoming a nuisance and therefore an impediment to settlement. Patience remains one of a successful mediator’s vital attributes.