Why is my AFCI breaker tripping and my surge protector clicking?
I've had some issues with AFICs in  the past, and one quick thing you should check (which ended up being my problem):
Is the insulation on the wire coming into the outlet box pinched and causing a loose/flaky connection? That will still give power to the outlet (under a normal breaker) and won't trip a normal breaker, but it'll drive an AFCI nuts. 

Another technique you can try to debug this is by swapping in a GFCI breaker, and see if that trips too. If the GFCI trips, it's a grounding problem. If it only trips on the AFCI, then there's arcing somewhere along the circuit. Check junction boxes, the outlet boxes and the connections to the plugs in the boxes.

Happy &amp; Safe Debugging!