I agree with several posters here - it is AA who dropped the ball when rebooked the party on the outbound - the agent failed to properly notate the inbound reservation or whatever code that is needed to revalidate the tickets for the BA operated segment on the inbound.

This kind of mishap happens A LOT. Usually the inbound disappeared long before the departure date. However in this case, OP's reservation was purged right up to 24 hours before departure. So there might be some other mishaps also involved.

I just wonder, given misconnect in today's air travel is very common place, what a travel can do to prevent the inbound segments do not get cancel automatically as a no show because the rerouted outbound did not get send over to the inbound flights operators? In this case, there seems NOTHING OP could do as the segment showed up online perfectly fine, UNTIL they were ready to check in for the flight - so what could he ever be able to protect himself on the mishap AA had done? Seems nothing!