Mrs LoM left her handbag on a plane in YVR just over a year ago and the actual BA ground staff were great once we established contact with them (she only realised after we reached our hotel in Whistler and she only told me about 12 hours after that).
The biggest issue though was being able to contact the ground staff at YVR to establish if anything had been found. The BA call centre were of no real help in giving contact numbers and Mrs LoM finally made contact after calling the main airport switchboard and then being routed through several other areas before finally managing to speak to a local BA agent.
It would have been easy to conclude that the item was simply lost although I am 99.99% sure that Mrs LoM would have been reunited with her bag upon check in for the return flight anyway, there would have been a lot of stress and domestic arguments about her stupidity
I don't think anyone can blame BA if items which are left behind are not found and they may even be missed during a cleaning cycle but being able to rapidly reassure passengers that their lost items have been located is something which could be done to really strengthen relationships between BA and it's customers. I know I always feel much more warmly disposed to an organisation that has helped me to deal with the consequences of my own stupidity