AA seems to take the miles out of your account instantly.

Unfortunately, putting them back in when cancelling an aaward (and paying the re-deposit) fee takes longer. From the couple times I have done it .. a week does seem a bit long, but yes it does take some time.

Apparently some of the 'process' requires more than one department to complete.

The only time I have seen mileage withdrawal not be instantaneous is when I used an eVIP one way and miles the other way .. again the statement was that it required multiple departments to be involved.