[quote]The initial directional velocities are randomly between 13 and 20 per time step. The radii are randomly between 15 and 50. [/quote]

It seems that your time step is too large (or velocity is too large).
Because you have particle moves 13-20 unit per time step, however, the radii are between 15-50.
So it is possible that the particle could move past half of the size of the particle.
However,  an approximation was made when I calculate the time particles really collide. (I have assumed that when we detect particle collide, the overlap distance is much small that their radii.
I think your problem will not occur again if you change velocity to 1.3-2.0