When you go to the Sounds and Vibrations screen, aside from the on/off switch there for DND, you should also be able to tap on the words "Do not disturb" to being up the different DND settings, one of which is "Turn on as scheduled." Make sure that's turned off as well. If it is and you're still having the problem, and we don't have any apps that might be changing the setting, then I would just try a full settings reset to clear whatever's triggering the DND (Settings > Backup and Reset > Reset settings).
