A few kernel versions (or Steam versions) ago, my Dual Shock 4 controller spontaneously stopped working in Steam. Big Picture mode said “no controller detected” and only games that had their own native DS4 support managed to still use it.

Looks like you need some udev rules to make sure all things are good. For my wired DS4v2 I stuck this:

SUBSYSTEM=="usb", ATTRS{idVendor}=="28de", MODE="0666"
KERNEL=="uinput", MODE="0660", GROUP="myusername", OPTIONS+="static_node=uinput"
KERNEL=="hidraw*", ATTRS{idVendor}=="054c", ATTRS{idProduct}=="09cc", MODE="0666"

into /etc/udev/rules.d/99-ds4.rules. And reloaded udev. Thanks Xard and others from Freenode’s #gamingonlinux for the pointers.