I have another data point about LA booking through Alaska.

I tried to book AEP>LIM>JFK and I got the "denied" error. This was showing a mixed cabin with AEP>LIM in economy and LIM>JFK in business.

Next, I tried booking only LIM>JFK in business. I was able to successfully ticket this flight.

I don't know exactly what happened. For example, there could have been a change in actual availability or synchronization between the IT systems between my failed and successful tries. On the other hand, I wonder if it could have been a glitch related to either the connecting flight or the mixed cabin.

Update: I was able to call Alaska and the representative added the connecting flight from Buenos Aires to Lima to the ticket that I booked on the website.

Also, just to add to this, I was able to call Alaska and the representative added the connecting flight from Buenos Aires to Lima to the ticket that I booked on the website.