Hola a todos. Tenía el mismo problema con mi Iphone 5s; seguí los pasos y se solucionó el problema.
I was having this issue too, it was always asking for the passcode even though the setting was on for iTunes & App Store. To fix it I turned it off and then back on again, it asked for my password and then it worked.
- Go to Settings -> General -> Touch ID & Passcode -> Touch ID
- Disable iTunes & App Store
- Re-enable iTunes & App Store
- Enter your passcode one last time
- It should work
Also as others mentioned, under General -> Restrictions -> Require Password might need to be set to 15 minutes.