I reported the following problem to EtihadHelp via PM:

Award seats in business (I class) are available from any EY destination in the USA to AUH, and from AUH to any EY destination in India, but I cannot book a connection from the USA to India.

(If the flights are within 4 weeks from the booking date there is no problem, connections can be booked. Outside that period, only trips that start and end in AUH can be booked.)

After I reported it to EtihadHelp, someone from EY woke me up at 1am (I had said it was OK to call until 12:30am) and asked me to explain it to him again. I did, and he seemed to understand it. After that, nothing happened.

American Airlines agents say they have also reported the problem multiple times to EY, but they have been ignored.

It is possible that the problem is intentional, i.e. that EY is allowing bookings that start or end in AUH (usable by Emirates residents) while not allowing connection bookings by people living in the US or India. But if so, this change should be officially announced and not implemented secretly.