Tecmo Koei has released a patch that fixes freezing issues in Dynasty Warriors Next. The issues involve the game freezing when it tries to connect to PlayStation Network under the Vita's current Version 1.5 firmware.
To get the patch, you'll just need to go into the Live Arena screen for Dynasty Warriors Next. You'll see an icon for the update. If you don't see the icon, you can tap the refresh icon and it should appear.
Sony's notice of the bug yesterday seemed to indicate that it would be fixing the problem with a firmware update. It's unclear if this is still the case.