Which is still probably not very long at all by everyday commonplace expectations. ((Amateur Scientific American reader guesswork alert!!)) The nuclear strong force simply stops being strong above a certain distance. Big nuclei are unstable because they are too big for the effective strong force radius. The stability that comes from jostling into a certain shape (and keeping the mutually-repelling protons apart) would itself be subject to jostling out of shape.
That's a p*ss-poor explanation of what's going on. The islands of stability actually occur where "shells" (distinct energy levels) are filled. As far as I can tell, this has squat to do with "contact between the protons"---a concept that I don't think has much meaning in the quantum mechanical world anyway.