iPad Air 2 Won't Take Screenshots
The screenshot happens when both of the buttons are released at the same time, so if you can slow down your movements and hold down the buttons for a short "two count" or long "one count" - basically a second and a half, then release both precisely.

If that doesn't work, you either have full storage or a problem with the system being able to process the button release events in a timely manner.

To troubleshoot that:


Put the device in AirPlane mode and power it off.
Power on the device and don't connect to any networks.
Open Storage and make sure you have 1 GB free or more.
Delete apps, connect to iTunes and make a backup if you have nothing you can afford to delete long term.
Once you have enough space free - try taking a screen shot in AirPlane mode.
If that still fails - erase all content and settings on the device (or restore it over USB from iTunes or similar tool.
If the screen shot still doesn't work after deleting all your content or restoring - seek service - there's something wrong with the hardware.


Depending on how much you deleted - restore your backup to the repaired / replaced / restored iPad.