I ran into this issue this morning. In the past few months I hadn't had issues having a seat assigned for my wife as a Gold benefit, but this morning it was refused due to data protection reasons.

I asked the agent if this was a new policy and was told that it was not - she said that she had worked there for 2.5 years and that it had always been this way. On digging further (on why I had been able to do this previously), it turns out the issue was that my wife had paid for this booking on her own credit card whereas the previous bookings had been made on my credit card.

The solution, as mentioned upthread, is for her to add me as a 3rd party to her BAEC account.