To reconnect a DualShock 4 with a PS4, you'll need to manually connect the controller with the console via the micro-USB to USB cable each controller comes with.

When troubleshooting a wireless PS4 controller, make sure that you charge to 100% first. This will make sure that you’re not dealing with a possible PS4 controller won’t-turn-on or weak ...

You can connect a PS4 controller using the micro-USB cable that comes with the device. But connecting a second one requires a different method.