Q: iMac suddenly fails to recognize my Apple bluetooth keyboard

First make sure the batteries aren't dead and that the keyboard hasn't already been paired with another device. If it hasn't, the keyboard should pair automatically when you reboot. You may have to press and hold the power button on the right side of an Apple keyboard until the LED starts flashing.

Otherwise see these support articles:

Mac mini (Mid 2011 and later) and iMac (Late 2012): Bluetooth keyboard may not pair during Setup Assistant

Apple Wireless Keyboard: Difficulty during pairing process

Unreliable wireless performance may occur when USB 3.0 external devices are close