How to (re)connect Magic Keyboard to Mac.

Is there anything I can do to connect my Magic Keyboard to my Mac? The keyboard is fully charged, it works fine when connected by cable, and it previously worked via Bluetooth. Now, though, when I unplug the cable and try to connect it to Bluetooth using the menu under the Bluetooth icon, nothing happens. I have a trackpad and mouse connected via Bluetooth, and they work fine. I've turned the keyboard on and off several times but I still can't connect it. Is it simply broken? I have only been using it for 2-3 months (although I purchased it over a year ago, so it is out of warranty). Thanks in advance for any suggestions. I'm reluctant to buy another one if they only last 2-3 months!