I also have this problem and it is apparently due to my having a Spanish name with two surnames (AmEx told me explicitly that the problem was a "name mismatch"). It is odd, because when I had a Spanish AMEX I was able to transfer both to Iberia and to BA without any problem. With my new US-based AMEX I can still transfer to IB, but my transfers to BA get cancelled.

I have talked to BA and they have asked me to send them a copy of my passport, so they will write my name the same way as it is there (but, as far as I could tell, it was already written that way).