Ok, good to know because you wrote it like you where sure, but now I see that you can't be.
I would think that it is a combination of foul trouble and stamina. In this case I had 6 players left and two of those had 4 fouls, if I remeber correctly, and the coach chose to put in the Lucky Fan. That is I had still an extra player so there is no real panic when it comes to fouls.
I had similar games without a Luky Fan enterring the field. As an example I had game where 1 player had five fouls and a couple of others had 3. Still the player with 5 fouls was kept on the field for most of the time. Thus, I think than there is more to it than foul trouble, but I do not know of course.