I have an iPhone 6 which never asks me for a password when updating apps, but my iPad 2 asks me for a password on every single app update if I want update apps individually even though I have the same restrictions settings on both devices (installing and deleting apps is allowed). Both are running iOS 9.3.2.
It's very possible that you've opted to "require always" at some point. To undo it, do the following:
- Launch the Settings app on your iPhone or iPad.
- Tap on General.
- Tap on Restrictions.
- Tap on Require Password under the Allowed Content section.
- Tap on 15 minutes (yours is likely set to Immediately).
- Click Settings.
- Click Touch ID & Passcode (May be named something else if you don't have touch ID).
- About 75% down the right column should be "Require Passcode" with an option to change between Immediately or not. If you have Touch ID enabled, you may only get the one choice.