Safety is the first priority. We've canceled for weather before, and we will again. The patients understand that the flight may be canceled due to weather, mechanical, or medical reasons. In some instances, pilots have been known to purchase commercial tickets or even drive the patient, if that's feasible. Sometimes a pilot gets sick or the plane doesn't pass preflight. A call may go out for a last-minute volunteer. But the short of it is that they are not guaranteed to make it there at a particular time and it is possible that the appointment will need to be rescheduled. And yes, it's possible that weather may permit you to make an outbound leg to deliver the patient but then be unable to return to base. Just like in any other GA flying.
There's a good video over at AOPA's ASF that talks about the responsibilities of what is called "public benefit flying."
http://flash.aopa.org/asf/volunteerpilots/index.cfm