When a neutron star accretes matter, will its mass increase? When a nova gets matter, the outcome is that it may lose more matter because of eruptions. Only some kind of nova's masses can increase stably. 

A white dwarf may become a supernova after it exceeds the Chandrasekhar limit, and we study that much. A neutron star can get mass too, why do not we talk about their end much?

How about a neutron star when it gets matter from accretion? It is necessary that its mass will increase? 
When will it collapse?
The neutron stars have about 1.1 to 3 solar masses. If the neutron star accretes mass, its mass will increase and once it crosses the Tolman–Oppenheimer–Volkoff limit, the star will collapse to form a black hole.

On way of this happening is in the case where one of the binary stars becomes a neutron star as in X-ray pulsars. The neutron star receives gas supply from its companion, which increases its mass,for example CenX3.



Source: nasa.gov

Though this method could lead tothe formation of black hole, no observational evidence exists as of today.