Are you sure they've actually been rebooked and re-ticketed?

I had this last week. Had the email saying inbound flight of a BAH booking was cancelled and BA would be in touch soon with options. MMB was then effectively locked out as you say, just a cancellation message and the BAH phone number.

In the end I rang them as the balance due date is approaching and I didn't trust waiting for BA to resolve it first. After much wasted time with the joke of their telephone systems, finally got through to a friendly agent who rebooked in a couple of minutes.

As soon as that was done I had an updated itinerary emailed and then MMB was back to normal functionality.