Regret the delay in updating -(I had hoped to receive a response from BA before posting), and my lack of providing specifics as commented on by several contributors - and correctly so.

We purchased AA return tickets on Apr 19, 2016: TPA/DFW/LHR/BGO -
BGO/LHR/CLT/TPA. All flights were serviced by AA except for LHR-BGO via BA and return on BGO-LHR via BA.

On June 20, 2016, our TPA/DFW flight AA 1198 was delayed by over one hour due to mechanical problems and consequently we missed our connecting flight AA0080 to LHR as well as our onward connection LHR-BGO via AA 6761 (operated by BA). We spent the night at DFW and flew to LHR the following day, June 21, 2016 via AA50 continuing the following day, June 22, 2016 LHR-BGO via AA 758 (serviced by BA). Whether this one-day delay could have caused the ensuing problems is unclear. AA arranged for our flights for the following day and the routing was the same, including the BA serviced flt LHR-BGO.

So yes, we had confirmed tickets and had seating assignments for all legs of the itinerary with the exception of the BA reservation on July 2, 2016 on AA 6760 which per BA rules could not be obtained until 24 hours before the flight.

And no, we were not able to check in for the flight to London - we were informed by the BGO SAS staff handling the flight that a) our names were not listed on the flight, and b) the flight was completely full. SAS staff provided us with a manifest which showed that our reservations had been canceled by BA/AA on July 1, 2016 at 2025Z. A copy of this was faxed to the DOT which likely helped make our case. A copy was also included in the faxed material to BA Passenger Relations. I don't know how to be clearer on this - we were unable to fly on a reserved and paid-for ticket. SAS expressed surprise and had no explanation as to why BA/AA would cancel us and why we were not notified.

With regard to what happened to the flight reservation itself? Everything was perfectly normal for a paid-for return ticket. We checked online for any changes in flight schedules before departing and nothing had altered. The only thing missing were BA's seat assignments which were not available until 24 hours before departure. It was then, 24 hours before our flight's departure on July 1, that we first noticed that AA6760 no longer showed up under our Reservation Code. The only flights that still showed were July 3, 2016 AA0731 LHR/CLT and AA1791 CLT/TPA. Since we were unable to find our BGO-LHR flight under our Reservation Code online, we contacted the Norwegian AA Rep to assist us in getting seat assignments. It was he who informed us that our "seats had been canceled." Although it made little difference, he did not say our reservations had been canceled. The end result was the same.

We have faxed receipts and documentation to BA's Passenger Relations and hope to get an explanation.