I had an interesting OLCI issue recently which I will recount in case it helps anyone else:

Background: I have an OTP-LHR-HEL...-PHX ticket, so a somewhat complex ticket with several carriers and codeshares issued by BA on BA ticket stock (ticket 125-...). To add to the complexity, one flight is an AY code on a BA flight, so I have two BA record locators for the same itinerary. This seriously confuses MMB. In case it's relevant, my BA account is also locked at the moment while some fraud is investigated, so I had to check in using the booking reference and passenger name rather than by finding it in my list of upcoming flights after logging in to BA.com.

The symptoms were that when I tried to check in using the BA website, I had a message to enter Advance Passenger Information. This did not surprise me, because this booking is not manageable with MMB (even when my account is not locked) so I haven't been able to enter API. I entered API for both passengers, clicked the submit/continue button, had an interstitial page, a refresh to the same interstitial page, and then I was back at a need to "Enter API".

I tried using the (Android) app with the booking reference and ticket number and this gave a different message that it needed the ticket number and I should contact BA if refreshing the app did not work. Unsurprisingly, refreshing the app changed nothing.

This sort of thing might make me think the ticket had changes, especially since AA are involved, but the agent on the Gold phone line was quite mystified. She could find nothing wrong with the ticket or the booking.

She suggested that she enter the API, so I dictated the information down the phone and she entered it. This mostly worked, she clearly got some anomalous messages but saved the information into the record.

I then went back to BA.com and was able to check in, although I was not offered any option to download the boarding pass but only the option to collect it at the airport. I'm assuming I can get it at LHR (or my B2B in OTP is toast).

So if you see the same situation, I suggest calling BA and asking them to enter the API and see if that helps. Some distinguishing features are: ticket does NOT need re-issuing or revalidation, itinerary involves the USA and is not straightforward, and BA.com appears to refresh the interstitial ("waiting...." spinner) twice before going back to the previous step to enter API.