According to Prof.Stassun in the Life and Death of Stars, neutron star sizes are limited by Neutron degeneracy pressure (and nuclear force) which states that the size of the star can be no greater than 3 solar masses. When the closely packed neutrons get closer, the heisenberg uncertainty principle would cause/necesitate the neutrons to move faster than the speed of light to balance the certainty in position. Instead they collapse into a black hole. Why would this collapse if caused by a star feeding it not produce a supernova just like the secondary supernova that occurs when white dwarfs are fed matter from a star greater than 1.4 solar masses but of the type produced by giant red giants that end up as black holes.
The reason why white dwarfs undergo supernovae when in an accretion situation is due to runaway nuclear fusion because they are unable to regulate their temperature as opposed to a normal star and so the resultant energy unbinds the white dwarf.
A neutron star in an accretion situation would just become more and more compressed until neutron degeneracy pressure is overcome and the neutron star falls into its own event horizon. A neutron star's matter is in a much lower energy configuration compared to a white dwarf (being held up by electron degeneracy pressure) and so ignition really isn't possible. Remember that white dwarfs are still composed of Carbon and Oxygen nuclei while a neutron star has no such nuclei for potential fusion or ignition.
EDIT: Time to address a very silly mistake. There are indeed nuclei on and just under the surface of a neutron star, most likely composed of Fe and other elements from the star before.
It is also possible for there to be fusion on the surface of a neutron star. If H and He accumulates to high enough amounts from a neighbor, then very brief runaway fusion (a timespan of seconds) can occur, which is detected as X-ray bursts. This is similar to the nova event of a white dwarf, and can occur periodically.