Likewise exactly the same issue had a four sector return including JFK-LAX-JFK other sectors posted Avios & TP fine tried to claim missing sectors online first, that got declined, after three phone calls to the always helpful UK GGL line have finally got them credited to BAEC, still battling with On Business.
Ironic as JFK-LAX is a flagship service for AA, as in AA0001 surprised they have not fixed this issue by now as it seems to have been going on for many months.
On a more positive note love the Flagship First dining option at LAX, had quite a tight connection so only used briefly on this trip but plan to fly later in the day next time so I can more fully enjoy the experience. BA could learn a lot from this
I find BACE online claim team seems to just automatically decline Avios and TP as a matter of course, making a phone intervention necessary. Does anyone else have similar experiences?