I also no longer receive emails from BA when I book or change a ticket. Even when I select the option to email myself the E-ticket receipt, nothing comes through. On the other hand, I did receive my first ever text message from BA the other day (other than the survey texts I get after most flights). They wanted to inform me that my flight from GLA - LCY would be operated by Jota aviation due to operational reasons (That'd been the case at the point of booking too).
Of course the famous Hilliergrams always get through. I guess there should be another any day now - I wonder what hand-picked offers or enhancements that will bring?