In Season 5 episode 3 of Person of Interest Fusco and Reese were saved by snipers who as Finch described were hired by Thornhill (the Machine).
So the question is, is there any rational explanation of why not to save Reese at the end with help from the same people?
Update: I am aware of the rocket launched by the submarine, but he could leave earlier with if he was helped.
There are several possible explanations in universe (and the other, obvious, one that this makes a satisfying, poignant ending for the plot.)
One important point is that the Machine and Reese have a deal. He reveals this in some related conversations when explaining his choices to Harold. But the essence seems to be that he has agreed that Harold's life is more important than his own and, if he has to sacrifice his life to save Harold's, this is fine by him. Remember, Harold's original plan for that final confrontation was for him to send the data without risking any more of his allies' lives. That would have risked Harold's life (which Harold might have been willing to do but neither the machine nor Reese were comfortable with). The only way for Reese to subvert that plan was in collusion with the machine. Given Reese's deal, the machine might prioritise Harold's safety, not Reese's survival and Reese would be entirely happy with that.
In addition, the machine is under severe attack at this point in the events and is losing even its basic ability to communicate with Harold (as we see as the episode unfolds). It might have no ability to coordinate other events in the real world and might, simply, not have the power to save Reese even if it wanted to.
