My giftcards.com orders didn't properly track a few weeks ago and I submitted inquiry for each one exactly as the 15th day passed. I received a response within an hour that confirmed the miles to be posted:

"Thank you for contacting AAdvantage® eShoppingSM. We have added the rewards for the following order to your account"

Furthermore, it said, "We understand that there might be a concern that the reward for an order will post after your AA deadline to achieve or maintain Status on your American Airlines account. Please note that American Airlines posts rewards to member accounts using the transaction date, so any rewards posting after the deadline with a transaction date on or before the deadline will still be counted towards your Status."

I was pretty surprised as I expected to go through a protracted fight to get the miles and LPs.