Dear PiO!
Thank you for your answer. Unfortunately, my intellect and experience is not as great as you might think.
In my experience, "neo-Catholics" have a more Catholic mindset than traditionalists who are led astray by a great number of errors.
Of course, it does not matter "how many times" something appeared in Church history, as we have to believe every teaching, may it be new or old (otherwise, we would be old Catholics).
Indeed, we must keep the faith alive and pure. But, after all, the Church is a visible institution.
Without a Church hierarchy, the Church will lose its Apostolicity. If the Church is no longer apostolic, she would no longer be Catholic. And if the Church is not able to provide another Pontiff, as the Roman clergy and remaining members of the hierarchy are extinct (soon) - she has not prevailed against the gates of hell.
An answer to these objections has not yet been given by sedevacantists besides the Cassiciacuм thesis or saying that there "some bishops out there with ordinary jurisdiction".