This article explains how to troubleshoot connection issues with wireless PS3 controllers.
How to Fix PS3 Controller Not Connecting to PS3 (TROUBLESHOOTING)
There are two official variants of the PS3 wireless controller: the Dualshock 3 and the older, discontinued Sixaxis.
Both versions connect directly to the console via a micro USB cable, and both have Bluetooth capabilities that allow for wireless play. Each controller also has an internal battery that charges when connected to the PS3. The only major difference between the two is that the Dualshock 3 has a vibration function.
Additionally, there are dozens of PS3-compatible controllers from third-party manufacturers. Some unofficial PS3 controllers only work when plugged directly into the console, and some come with a Bluetooth adapter that you need to plug into the console to play wirelessly. Nevertheless, they all rely on the same underlying technology, so they’re prone to the same issues. PS3 controller connection issues can be caused by: