Why does my surface pro 3 keyboard stops working

I do not have enough knowledge about surface pro because I am an ios user. But it seems like there is some software or operating system issue. That's why it stops detecting your keyboard and sometimes it got detected. You should reinstall once your OS before applying any hardware things.

The SP3 keyboard failure is a common one that happened about the time you asked this. All attempts at solving it have failed - restoring Windows, updating drivers, even replacing the keyboard with a new one. The only solution I've found is that there are several vendors on Amazon and such selling what look like the Microsoft keyboard but use Bluetooth to connect to the SP3. They also use USB-C to charge their internal battery. Otherwise are essentially form, fit, and function like the SP3's original keyboard. And far less expensive, too! They still attach like the original but can be used even across the room.