It'll most likely be profit (or lack of it) if they made it a codeshare. To make it eligible for a codeshare, it needs to be suitable for both parties and they both need to make money from the agreement - on this route, I don't think they would.
I don't think an IB codeshare would make a massive difference on the load factors. You're forgetting that their reservations agents could easily book it under the BA flight number if they wanted too anyways, just like BA can for non AA codeshares etc.
Sometimes I wonder why they're keeping the route going. Apart from the odd full flight, it's generally less than half full. I agree it does take time to get routes off the ground but with the schedule they've got I can not see it ever being a great route for BA.