An interregnum between Popes is vastly different than a claim that the See of Rome has been vacant since 1978, or 1963, or 1958, or whenever.
"If anyone the says that it is not from the institution of Christ the Lord Himself, or by divine right that the blessed Peter has perpetual successors in the primacy over the universal Church, or that the Roman Pontiff is not the successor of blessed Peter in the same primacy, let him be anathema." (Vatican I, Dogmatica Constitution on the Church, Chapter II, Canon)
Its tough to see a 48 year gap as "perpetual successors", especially when there have been four claimants universally acknowledged by the Church, and especially when Catholic theologians have long taught that the acceptance of a claimant by the Church is a fact closely related to revelation - it is termed theologically certain, denial of which is a mortal sin against the faith.
See for example, this Sedevacantist page on John Lane's website, which uses as an example of this theological note "Legitimacy of Pope Pius XI" to illustrate "a truth logically following from one proposition which is Divinely revealed and another which is historically certain."
http://www.stthomasaquinas.net/theolnotes.htm
I never said anything about previous Popes. I just wonder whether the Seat is currently vacant. It doesn't really matter all that much because in this era of collegiality he might as well be Pope emereitus John Paul II.