CX doesn't have a middle name field in their reservation system, so even if you have your middle name on your AA profile it won't show up on the CX reservation. Instead CX has a given name field which is used for both first and middle names. If you ask AA to put both your first and middle names in the first name field, your middle name will show up on the CX reservation. I have traveled on CX without my middle name on the reservation, however I could not OLCI as I got an error that the name on the reservation didn't match my passport.