I've read Fr. Reilly's writings earlier and I agree with him for the most part.
Clearly, once it is established in principle that a long interregnum is not incompatible with the promises of Christ, the question of degree - how long - cannot enter into the question.
The following is a good example of why laymen should not try to practice being
a theologian:
Yes, that is the typical argument, but it can be reduced to absurdity in various ways, which I won't enter into now. But what I'll say is the proof of a natural limit to an interregnum comes from Catholic doctrine, implied in Pope Leo XIII's teaching and laid out in Pope Pius XII's teaching as well is that Bishops receive their episcopal office and the ordinary power of jurisdiction along with it not in virtue of their consecration alone, nor directly from Christ, but rather immediately from the Supreme Pontiff.
This affects the nature of episcopal consecrations during an interregnum and deprives those thus consecrated of an essential power which would otherwise be proper to them. If the Church were thus to continue in this way for too long a time, it is evident, that the transmission of ordinary jurisdiction would cease, which again reflects God's most wise design in constituting His Church with the person not just the empty office of the Pope essential for said transmission. But jurisdiction is a requirement of Apostolicity, and it is of divine Faith that the Catholic Church is Apostolic and cannot cease to be so, as she would have, if there were no orthodox Catholic Bishop in the world possessing ordinary jurisdiction. Hence the notion of an indefinitely long interregnum is assuredly incorrect, and would probably merit some censure, most likely at least "erroneous in theology" for being the contrary of a dogmatic fact.
I just wrote a [lengthy] response to you and deleted it by mistake 
I will just say, I like that you stay on the subject and respond logically. It is very refreshing. But I am rather frustrated at myself right now. Perhaps I'll come back again and try it all over again some other time.
Sometimes that happens to me, so to avoid the problem, I have found that by
typing into another program (I use Notepad because it's lightweight and uses no
RAM to speak of) I can then save and update my words, and then when I'm
ready, just paste them into the REPLY box here. It takes a few extra steps
but it
saves a lot of grief. It also helps to see the words in three different views so then
I can find typos or missing words, etc., more easily before hitting "Reply."