My controller does not work unless plugged in with a USB cable

My PS4 controller is connected to my PC with Bluetooth. The controller works with some games that I downloaded on Steam: when I turn it on the controller has a blue light and allows me to play as much as I want.

However, I downloaded a game off of a website and my controller only seems to work when it is plugged in with a USB cable. I've tried countless times to pair my controller via Bluetooth but while it says the controller is connected, the controller doesn't stay on for more than 5 seconds before automatically turning off again.

How do I keep my PS4 controller connected wirelessly? I'm using an Alienware Aurora gaming PC.

To access all the functionality of a DS4 on Windows you need a driver. Steam has an internal driver that supports Playstation controllers. If you add your game to Steam as a "Non-Steam Game" then it can use Steam's DS4 controller support.

Alternatively, you can use unofficial third-party drivers like DS4Windows that create a virtual XInput device for use with non-Steam games that need XInput.