I've had this on 4 out of my last 6 flights out of LHR and no ones been able to explain to me (on the phone or at the desk) why. Most recent of which being BA912 tomorrow.

The return is always fine on the app again but at LHR I have to go to the kiosk/First Wing to check in.

Only seems to be hitting me at T5 as well. The two I had from T3 allowed me to check in without issue

It's a right PITA.

Once checked in at the desk however the app will quite happily let you get the BP. First time it happened I was worried about ticketing and BA over twitter were happy to confirm all was well.
They didn't seem to know much about it either. Agent on the phone also unaware of what was causing the issue.