I think the answer to that one depends on the fish. Some species must graze contually throughout the day or should ideally be fed twice or three times a day, where others can go a day or two between feedings on a regular basis. So I would say weeks to months for any given fish to starve to death, but just my layman opinion.
Same goes for lifespan, some fish can live for 10 years or more in a good environment.