Hogwarts will, and must, reopen. Reopen isn't even the right term, as the school never closed, just changed hands. When times are the darkest they've ever been, people will need a place to turn to, and to learn how to protect themselves. Hogwarts will be that place.
As Harry and other point out numerous times throughout the series, there isn't a safer place than Hogwarts. Why would it close, when it can protect so many people?
Another reason for it to stay open is information. Harry and the gang will need all of the help they can get, and Hogwarts is full of free information, including the new protrait of Dumbledore, which may or may not be able to help the trio in their quest.
Who knows..maybe there's a horcrux or two lurking inside!