Go to Settings>iTunes & App Store>Password Settings. Try unchecking the password setting there.Demo, in my iPad Air (not a 2) it does not show that setting.
Demo, on my iPad Air (not a 2) it does not show that setting for some reason. In Settings > iTunes.... I see my Apple ID but no Password Settings. Under it, it says "Manage your PW settings in Restrictions....". In Settings > General > Restrictions (after the code) I can see the Allowed. Perhaps our devices are different, but same iOS ?? 8.4.1 (12H321) ?. I have All Settings set to Green under Allow.
For the OP, I would recommend that All be allowed except In-App Purchases. Then look down under Allowed Content. Click on Apps and check the age ratings. Then check Password Settings > Require Password > Turn it OFF. This last setting may well be the reason.
Hope this helps...