I'm having the same issue, but on Firefox, I'm only able to select seats on Chrome. Once you click through to add info (past the flight selection), it creates a temporary record locator that's on hold so you can add all the info and pay. If you back out, it's automatically cancelled.
I believe that if you get through to the seat assignment step, AA.com creates a locator that is temporary. You can book it but it could disappear at any moment. I had this happen when we were using Chrome to book seats on an award ticket. We closed out but we saw that a record locator had been created. With a 1 day hold as opposed to the traditional 5 day hold.