The lapse of time during which a given event has not happened, is, in [the] logic of habit, constantly alleged as a reason why the event should never happen, even when the lapse of time is precisely the added condition which makes the event imminent. A man will tell you that he has worked in a mine for forty years unhurt by an accident...

Not to get too nitpicky, but the mine example doesn't really work here. Working for 40 years in a mine without accident doesn't actually make disaster imminent; I would imagine that a mine disaster is a Poisson process, in which expected duration to the next accident is independent of any previous occurrences.

It seems like there might be some gambler's fallacy stuff happening here.

An actually good example of this would be a bridge whose foundations are slowly eroding, and is now in danger of collapse.