I'd guess that it has something to do with the internal structures of protons and neutrons.What exactly causes this instability? Neutrons and protons have roughly the same mass, so there's not much of a potential energy difference between di-neutronium and deuterium, and from my understanding, the strong force affects all particles with the same amount of force within a certain radius, so they're no more tightly bound than one another. Also, there is no Coloumb repulsion in either, so what causes the nucleus to decay?
As I recall (and I'm doing this by memory, so someone please let me know if this is correct), the quarks of a neutron have charges of +2/3, -1/3, and -1/3, for a total of 0. So, packing several neutrons together would be tantamount to having several negative charges right next to each other. So, a neutron in those conditions would spit out a negative charge and become a proton.
But as I said, that's just my best guess.