During the UAL pilot's job action fiasco of 2000 it was very common for people to miss meetings, if not entire conferences. I don't think there is any refund rule pertaining to making any scheduled or non-scheduled event.

For example, in the "USA Today" they had a story about a man who traveling from ORD to LAX to see a dying parent. His original flight was canceled due to the job action and the gate agents refused to give him waitlist priority for subsequent flights. He finally got to his destination several hours late only to find his parent had just expired. He wrote to UAL and was given only a $100 travel coupon. If you're a frequent flyer you may have better refund luck, but they might just tell you to fly the evening before next time to take into account schedule irregularities which do occur.