They lost the ability to wield it, hence until 1999, they were forbid to touch it. IGA said that there was "something" that happened after SotN which "caused" the Belmonts to forfit their vampire hunting duties until 1999. Until then, they'd hand over the Vampire Killer to the Morris clan. They DID willfully pass it, but they, themselves, couldn't touch it. And there is a "reason", but only IGA has the idea to "why" this was. The only hint we have is that it's something that involved Richter(who's the last main branch Belmont to wield the VK).
And it's my opinion, but I would think if IGA did make this game(which is likely to happen someday), it would be the final piece in the Dracula X trilogy(not counting Dracula XX).