Why do I have to reconnect my Dualshock 4 everytime I use my PS3?

I don't have a PS4 in my house. Whether I turn on my PS3 with the DS4 plugged in or unplugged or if I use the PS3 power button or the DS4 PS button to turn the console on, I always have to delete and re-add my DS4 in Accessory Settings. Anyone else have this issue?

Is there a proper way I should use it? I prefer to use it wired but even using it wireless this issue still happens.

Here's a short video showing what I mean. https://www.youtube.com/watch?v=LBumP8jPbFA

Plugging it in makes the lightbar^TM thing blink orange. This happens everytime no matter what I do. I hope I'm just doing something wrong and don't have a bad controller or something.