Once we almost missed the flight (I think this was SMF) because of a combination of factors, mostly long lines at any conceivable waiting spot.... we actually RAN to the concourse with car seats and 3 kids in tow and got there as they were boarding the last section. I suppose that might be "not even close to missing the flight" by some people, but that was way closer than I would ever feel comfortable about it happening.
I haven't had an incident like that since, so I guess it was just the odds game....