I'm presently encountering a similar BA/IB Avios booking nightmare...
Bottom line: previously ticketed Avios booking on Ibera has been cancelled by BA twice, and they are unable to reinstate the flights or provide any meaningful alternative options.
Made a Avios booking on BA.com LIS-MAD-SJU on IB J a couple of weeks ago. Immediately received confirmation email with ticket number. Contacted IB for seat assignments and subsequently received a separate confirmation email from IB (with same ticket number). The next day I went to the IB webpage to print the itinerary, and there was a note the reservation had been cancelled. Contacting IB, they said BA had cancelled the reservation. I called BA Executive Club who confirmed the reservation had been inadvertently cancelled by the system because a reference code was not stored in the right field. The BA agent restored the segments (there was still award availability at the time for both segments) and sent another confirmation email (containing the same original ticket number). The agent told me that this is a known issue with IB awards booked online and that I should have "known better than to book on BA.com" and should have called in to book this award and paid the extra booking fee. His tone was rather condescending, but he assured me that the booking had been fixed and this wouldn't happen again. I followed-up with Iberia who confirmed the reservation looked good on their side. Over the next several days, I watched the reservation closely on Iberia.com, BA.com, and setup EF alerts for my seats (in case they were vacated) and the reservation remained intact.
I spent the next week without internet access trekking in Nepal. Upon my return I noticed I had received an EF seat alert that my seats on both IB flights were now available. I was unable to pull up the reservation on Iberia.com (received the same cancellation message) and calling Iberia they confirmed the reservation had been cancelled by BA. Calling BA, they confirmed the reservation had been cancelled "automatically by the system" for the exact same reason as before (a particular field in the booking was missing a code). They have attempted to have the segments restored with Iberia, but have not yet been successful. For three days, BA has told me to check back the next day but so far nothing has changed. As these flights under a week away, I am running out of time and patience. Yesterday, the BA agent I spoke with (coincidentally, he was the first agent I spoke with over week ago who was supposed to have fixed this in the first place) suggested that I should start "exploring other options" and that BA could refund my ticket but wasn't obligated to accommodate me on other airlines (AA has routing that would work, but currently has no award space available). I was told to check back again in another day to see if IB had opened up space (doubtful considering the MAD-SJU flight is now J0).
I have now spent over 6 hours trying to resolve this issue (mostly spent on hold) without any success. Just looking to see what my rights are in this instance, as I cannot get a straight answer from the Executive Club agents. Is BA obligated to get me from LIS-SJU (even on an offline carrier) or can they just cancel my ticket and refund the Avios/taxes without my approval? Does this qualify for EC/261? If so, do I need to physically show up at LIS and be denied boarding for my originally ticketed IB flight? I have found award space on TP/UA that I can book, but I'd like to know exactly what BA's obligations are in this circumstance.
-FlyerBeek