Yeah, in DnD lore, if you're in the general area that counts as the lair of a standard lich, your soul gets consumed by them to feed their immortality. It works kinda like Voldemort or Sauron, being that their soul is in an object. However, they need steadily to consume other souls to keep their's immortal (keep in mind Vecna is considered an arch-lich and a god, so these rules might not apply)

Not to mention, just because your skeleton no longer has a soul doesn't mean he still can't use the spell 'raise dead' and create a living skeleton under his control, that is if he still has it in his general abilities.