It looks like CBS in no longer interested in keeping this show in its lineup after the upcoming 5th season ends.
From what I am reading it looks like a number of factors are at play here. First off, Sarah Shahi was offered the role of Nancy Drew for a new pilot so this would be her final season.
There are also business issues to consider. This is a comment from the story.
Note that CBS does not own Person of Interest, therefore makes no money from DVD sales, syndication, etc. Each network obviously prefers to own the shows it airs in order to make as much money as possible.
From what I am seeing in the comments there is also a lot of complaint about Carter, played by Taraji P Henson leaving for Empire. I have only seen a few episodes of season 1 and don’t want Empire so I didn’t realize she played Carter. From what I am reading Carter is still popular and a lot of fans wish Taraji had stayed on.
This is one of those “Sad but inevitable” stories. Poi was such a unique and different show that it was probably doomed for a limited shelf life. Hopefully now that the writers have forewarning they still have time to write a decent ending if they haven’t finished shooting season 5.