Would all neutron stars inevitably collapse into black holes due to quantum tunneling?

The materials inside a neutron star are densely packed (extremely close to each other) and as time goes by say about an eon later, most of the neutrons would eventually tunnel into each other

Based on what ?

The material's collapse was halted from an astonishingly high speed collapse by the neutron degeneracy pressure that exists precisely because the universe doesn't want to let two neutrons fuse. The enormous forces involved in the collapse and the enormous forces keeping the mass compact are not high enough to overcome this. That's why it exists in the first place.

Over time "tunnelling" works in many, many ways. If two neutrons were to fuse in this manner the list of possible by products is enormous, and a black hole is most unlikely, IMO. We've a lot of experience of whacking particles into other particles in extreme conditions ( think CERN ) and we haven't seen any sign of a black hole yet ( and believe me, they're looking for them ). So I think the odds of a fuse into a black hole are extremely low. Over time it's more likely the neutron star would "evaporate" into other particles. But over those time scales you're looking at the cold death of the universe and protons decaying and so on.

And if, for argument sake, a mini black hole formed from two neutron's "fusing" it's life expectancy would be minuscule as tunnelling effects ( predicted by Hawking ) suggest it would "evaporate" in the blink of an eye. So isolated fusing events, even f they happened, would be unlikely to produce a black hole that grew, but instead one that just blew up as fast as it was created.

and voila! the neutron star becomes black hole? sound suspicious to me but can it happen?

No evidence I am aware of suggests neutrons will fuse in the manner you're describing.

"Neutron Star" is probably something of a misnomer. Apart from neutrons, current models ( "educated guesses" ) suggest that the core of such a body might be a lump of something called quark-gluon plasma, which is essentially mush made from neutrons. This is what you get when you fuse neutrons together - a form of mush made up of the stuff that neutrons and protons are made from - quarks.

So theory and evidence suggests that you don't get a black hole from just waiting for a neutron star to change into one.