It's not new or unusual for EF and BA agents to see different availability. Both are front ends to the core data, and BA agents have a different front end to you. POS is the usual explanation but you seem to have ruled that out. There are also time lag issues. Sometimes it's failing to understand any connecting flights and their rules. Sometimes it's because even though D is available there aren't any D fare basis available (though that should not affect a DONE booking). It's usually best to ask the agent to find the next nearest / best alternative, then try again to rebook a few days later.

(For the benefit of those trying to understand the question, the OP has a Round the World ticket on oneworld, which in business class books into D, hence known as DONE)