I experienced something similar a few days ago. I had a VIE return booked for July. Indeed, it had originally been booked for April, then re-booked at least three times through May and June, but given the nature of the trip I am able to easily keep re-booking, which I did.
Anyway fast forward to last week and I received yet another cancellation notice, but this time I was unable to re-book on MMB and was instead directed to call BA, which I did. I was then moved on to a flight the following day- I must say that the call and the re-booking all went very quickly and easily, and I did not have to hold at all- not sure if I am just lucky or whether they have got their act together, but credit where it is due. I can't shed any particular light on why I had to call rather than being given the opportunity to re-book myself on MMB, but I can say that the OP's situation is not unique.