Seat issues are not uncommon between finding, holding, booking and during the interim between booking and flying. There may be various reasons this can happen.
Seat held, changed or gone at booking: One member theorizes a held seat may be taken by a positive purchase by another passenger. But it could be due to another factor listed below.

Disability designated seat: Some seats are assigned preferentially to people with disabilities, and their companions, under the Air Carrier Access Act. Even some non-disability seats may be required for a person with a disability in some conditions.

"American blocks a limited number of seats on each aircraft to accommodate customers who identify themselves as having a qualified disability. Adjacent seats are provided, under certain circumstances, for customers with disabilities who must travel with a companion for assistance."

Flight nearly full: Once a flight has reached certain capacity guidelines, no further seats will be assigned. This leaves airport staff room to deal with the needs of persons with disabilities, no shows, delayed connections, etc.

Boarding pass scan fail: Sometimes a boarding pass scan fails (listen for the "Beep!") and your seat may register as no show, so another, later Passenger or standby gets your seat too.

Equipment change: AA Information Technology's very inefficient at these. You may have selected a Main Cabin Extra as an elite, yet a change from one aircraft subtype with differently numbered seat rows to another and you may find yourself moved from your carefully selected MCE aisle seat to a middle seat in one of the last rows. Aircraft substitutions from one type to another (77W to 772 or v. v.) or even "downgauging" (767 to 757) may occur - this will generally result in unanticipated seat changes.

Equipment malfunction: A seat may not be available on a specific flight because it was reported as malfunctioning and has not been repaired yet.

Crew rest seat: Some seats are contractually required to be set aside for resting crew, on flights of specific lengths.

Federal Air Marshal ("FAM"): FAMs are generally accommodated in the highest class of service in seats that are often popular with passengers. These accommodations may occur at any time, and by law AA must both comply and not reveal to passengers the reason for their seat loss or change. That's correct: AA is prohibited by law from telling you your seat was given to a FAM, so you will only hear implausible and made up reasons of how you lost your seat.

Other: AA might be required to seat a passenger with a small child together, displacing another passenger. There may be other reasons as well.

It is suggested you regularly check your itineraries to deal with route and flight changes (often unannounced) and seat changes (always unannounced).

Link to thread detailing use of Twitter for contact with AA (some have used for seat loss remediation)