Update: Whoops, David got there first!
In a new paper published in the Proceedings of the Royal Society, researchers from UC Berkeley reveal that shoelace knots do not gradualy come loose, as was previously supposed — rather, they fail catastrophically and suddenly, thanks to strange and surprising stresses that they must endure.
The researchers used high-speed photography trained on subjects on treadmills, and attached accelerometers to the tongues of the subjects' shoes. From this, they discovered both the sudden failure of knots, and the explanation for it: 7 gees' worth of stress.
Further experiments demonstrated that simply stomping up and down wasn't enough for a knot to fail; neither was swinging it back and forth. It took the interlaced effects of the two forces to undo the knot: the repeated impacts loosened it while the changes of direction pulled on the laces.
The roles of impact and inertia in the failure of a shoelace knot
[Christopher A. Daily-Diamond, Christine E. Gregg and Oliver M. O'Reilly/Proceedings of the Royal Society]
Unravelling why shoelace knots fail