Though our last BAH was a year ago, IIRC I got both an email and a text reminder about the balance being due. A long time ago (must be over 10 years ago) I missed the balance date and called in two days later to pay it. Though I got told off big time, I saved the holiday. Phew! YMMV.
A day or so you may find BA being sympathetic, but more than that is taking the ‘p’ IMHO.