Ok some useful info from BA’s online chat, thanks to Sophia for this:
“Hi there, there is indeed a technical issue with the balance booster tool this morning. The relevant team are aware and are already working on resolving this. I will pass on your membership number as we are currently giving them numbers how many customers are affected. I would advise to check back with us in a few hours or attempt to boost again in a few hours.”

I asked whether it’d be a case of hoping it’s resolved before 23:59 GMT, or whether it would be extended – this hasn’t been decided yet, and Sophia couldn’t commit to anything either way, which is fair enough. But at least BA are aware and doing something with it.