As of now the New Horizons probe is well beyond the orbit of Pluto, moving towards the Kuiper belt. In an article I read that New Horizons will eventually follow the path of Voyager probes to the interstellar space. But how long it will remain functional and as further it will travel away from us it will also required very long time to receive data from the probe. Is there any pre-planned fate of the probe ?
The answer is in the other section:
What I can say off the top of my head is that the mission has been extended and they have identified another object that the spacecraft can reach. However, after the next rendezvous it will be out of fuel and will not be able to maneuver. BUT -- the probe is powered by a Plutonium-238 radioisotope thermal generator (RTG), and will likely to continue functioning for the foreseeable future. The relevant question is: how long will the government fund the NASA operations team that is 'talking' to the probe. That is anyone's guess.
PS - I'll update this answer later once I talk with some colleagues. I started, and worked for the company (KinetX, Inc) that did the navigation for New Horizons. I no nothing of the science, but my friends did the navigation and know the near-term details for the mission.