If you have followed all the best practices outlined in What are the best practices for using AAdvantage eShopping, you may be able to escalate your missing miles case for additional review.
This may happen when AAdvantage eShopping responds with:
The merchant has concluded the research on this transaction and has notified us that this order is not eligible for rewards.
Merchants on our site attribute orders to the last touch and pay commissions to AAdvantage eShopping. We then convert that commission into rewards that we post to your account. In your case although you started the purchase while logged in to your eShopping account, the merchant has indicated that the last touch before you completed this transaction was not https://www.aadvantageeshopping.com and therefore the commission for this order did not track back to your eShopping account.
Based off this response, you can reply:
I would like to request an additional review by a supervisor. As evidenced by this recording [link to the screen recording], there is no possible way commissions were paid to any other affiliate.