Actually, you'd be hard pressed to find a FAA reg that says an airline must operate a scheduled flight - it doesn't exist. As I've said before, though, airlines don't cancel flights just because of light loads but if a cancellation is necessary they will attempt to cancel a flight that will inconvenience the least amount of people (considering all factors - type of plane, downstream schedule/loads for that plane, crew availability, etc). So you may have a perfectly good plane with crew sitting at your gate and your flight get canceled - they use that plane (and maybe crew) for another flight whose plane had a mechanical, was stuck somewhere because of weather, etc.

The Shuttle is a little different because of the frequency and where it operates. If flights start getting backed up because of delays, they will at least look at canceling one or more segments in an attempt to get the later flights on (or closer to) schedule.

I suspect this is what results in the perception that flights get canceled because of low loads.

Jim