Facing the same issue right now. Entering my 16-digit AAA number, and I get the "Invalid AAA/CAA card number" message. 🙁
I saw this post on this thread a couple of years ago and I copied it to my notes. So if it doesn’t accept my number, I use 429 or 620, my CDP and the rest of my number and it always works. I do have my actual card with me when I check in but this at least lets me make the reservation.
https://www.flyertalk.com/forum/29638637-post423.html
Based on some testing, it looks like it will take 429 + valid Club Code (CDP) + 10 digit number. CDP #’s can be found on sites like Hertz and other websites (if only a two digit code, add a 0; not sure about those that are more than 3 digits). Also tested with a CAA number and it is fine.