Oddly, it let me check my upcoming flights all week, and then it let me check-in today, but then the app suddenly discovered that it's not supposed to work, and won't let me collect my boarding pass on my mobile. I repeatedly got the same extremely lame message on the app as the OP. "Sorry, we are currently unable to log you in or retrieve your upcoming flights. Please retry later. " - which sent me to Google to find out what was going on here. So without a printer on the road for the email version, and with no means of collecting an SMS boarding pass.
I'm not at all surprised at such indifference from BA when it comes to customer service - these days, it seems typical that they wouldn't advise their clients that the app was being retired. Maybe they'll blame it on a power failure. They have fallen off the shoulders of the giants they were once standing on, and are now being trampled. "Alex" and the rest of the Iberian team must be giggling themselves silly at being able to discredit the British and finally get even for all that fuss about the Armada back in 1588.
If BA can't be bothered to support its customers, then it's time customers should wonder about supporting British Airways.