"We're not resurrecting the Gods. They were always here. We're renewing communion with them."
Alright, so apologies for the length of this reply but you ask a fair question and a fair question deserves a thoughtful answer.
I think you can divide pagans into four groups that aren't all mutually exclusive. First you have those who acknowledge there's been a break in the tradition and those who don't. And then you have those who, assuming there is a break, view the break as a fundamental problem and those who don't.
So some pagans outright deny that there's been a true sundering and assert that those who practiced their ancestral religion just went underground and continued in secret. In the world of Greco-Roman paganism, groups like Pietas (Roman) or YSEE (Hellenic) have this approach. They can cite anti-pagan laws in Late Antiquity through the Middle Ages, trials of those found worshipping the old Gods, and so on. This is certainly evidence, but evidence of what? It could be people periodically seeking to reconnect to a lost inheritance just as well as a continuing religious practice. Scholars like Ronald Hutton usually dismiss claims of the latter. Then you have others who have a softer version of this argument, pointing to pagan survivals such as people in Scandinavia continuing to leave offerings for the elves into modern times. Or, speaking as a Romano-British polytheist, an example would be coins still being offered at the Roman baths at Bath, just as in ancient times. (Replacing offering a prayer to the deity with simply making a wish.) Then there's holidays and so on that supposedly retain many pagan elements. Me? I go with the scholarship, and am skeptical of claims of a direct pagan line of “apostolic succession”. But admit that the evidence would look the same either way.
Okay, now there's the question of whether a broken line should matter or not. For perennialists/traditionalists, then the answer is yes it does matter. I personally don't think it does. We're not resurrecting the Gods. They were always here. We're renewing communion with them. If you lose a friend's phone number, the fact that you can't call them doesn't mean they're dead, only that you are out of touch with them. For us, the old language of rituals and rites is the "phone number", the means to re-establish this line of communication. The challenge is that the evidence is spottier in some places than others. The Romans preserved more information on rituals than the Norse/Germanic peoples. Where it would matter however would be the mystery rites like the Eleusinian or Mithraic mysteries, which were initiatory and are now lost for good.
So I would say the point you raise is a challenge, but not a fatal blow to the project of renewing the Pax Deorum.