When AFCI's first came out there was many problems with them and tripping on inductive kickback from inductive loads such as the big transformer in a microwave was one of them, from what I have heard they got better (Indiana took out the requirment for AFCIs way back in 2005) also the earlyer Square D home lines were notorous for this, and they did a recall, which you can tell which one it is by the test button color, If I remember right the bad ones had a blue test button and the new ones had a green one, (maybe someone will verify this)
Also check the micro cord with a high reading ohm meter, if there is any leakage from the hot or neutral to the grounding conductor, it will cause the AFCI to trip, also inductive kick back trips happen right when the inductive load is turned off, if it is tripping when the load is turned on then it could be a grounded neutral in the circuit feeding it.
just some food for thought.