It was the third stroke.

Alice here: For over two thousand years the "third stroke" has meant your last chance.  You can find this expression in way back in Aeschylus, and I think that through some crazy connections it's behind the "three strikes and you're out" rule in baseball.  A hopeless drowning victim is one who has gone under for the third time, etc.

Given its context of this story, and without meaning to do anything other than leap this phrase up the levels that we've talked about, it's clear to me that on the mythic level the word "three" can also suggest the Christian Trinity of Father, Son and Holy Ghost. 

That would be a gratuitous association, I'm sure, if this story and the strokes didn't involve a Roman Catholic Priest.  But I doubt that Joyce used the expression "the third stroke" carelessly.  No reason to speculate farther, at  this point--we're only on the first sentence of the story.  But we ought to watch to see if this story plays out on the mythic level as well as on the realistic one of physical paralysis. In other words and without the shorthand of "levels" I'll phrase it this way:  is the priest simply dying physically, or is he dying spiritually, too? This first sentence doesn't give the answer, it raises the question.