Was it BA or handling agent staff?
If handling agent, then their hands are tied and they have no
authority to bend the rules. If BA's own staff they may have been able to
us the value of the ticket as a credit towards the new fare but this is not
normally done if the flight has departed.
If BA have changed your ticket free of charge in the past it may have been because the flight you were on was overbooked and it was in their interests to do so.