There was no hope for him this time: 

Alice here: "No hope for him" tells me that's he is about to lose, to be a failure, but the abstract language leaves open the question as to in what sense he will be lost.  The man is likely to die because he's sick and has had two prior strokes, and probably soon--so there is no hope that he will cling to life for very long.   But what if there's more to it?  What if, even after his physical death there will be "no hope for him" --if there is any truth in this implication, then from a Catholic point of view (we are soon to learn that he is a Roman Catholic Priest) this time he may soon lose his soul.

"This time" suggests that there have been other times.  We know there were two prior strokes, but beyond the physical, were there two times when the Priest is in danger of putting his soul in danger?. When this story is done, think back on this: what were Fr. Flynn's first two crucial times, when he put his soul in danger? Does Joyce let you guess right?