My partner and I flew LHR-JFK in December, and were promoted to Bronze after the outward flight – or at least should have been.
BA accidentally recorded the outward leg as an ‘ineligible flight’ and despite several emails, it was not corrected until some weeks later.

On the return flight we were in WTP, and so when we came to select our seats, it wanted to charge us £60 for the privilege, when we should have been entitled to free seat selection. But by T-72 (days after we'd asked them to fix the problem) there were only two seats left together in the cabin, so we reserved these two seats and paid, assuming that BA would subsequently refund the £60.

After two emails to BAEC customer services which received no response and a month of waiting, BA have credited us with the Tier Bonus for the return leg, but just sent us a very dismissive email saying that they won't refund us the £60, and they are sorry they can't help further, with no explanation of why.

This has confused us. Surely if they are accepting that we were entitled to free seat selection, and that it was their mistake that led to us being charged for it, how can they refuse to refund?
Any advice before I take it further? Are we not in fact due a refund? Have we missed something?

The dismissiveness of BA's reply and refusal to even explain their logic after a month of waiting has astounded us!