Here is the next reply from web services:
American Airlines uses the verbiage "24 hours" to mean by 11:59pm the following day. In normal circumstances we will always hold a reservation until 11:59pm the following day.
So that clears up any confusion about whether I might've missed out on the fare due to not booking within 24 hours. (I'm glad AA has its own definition of what "24 hours" means...
)
I think the problem was PDT vs. CDT, no matter what the web site said. To avoid problems in the future, I guess I'll just try to book by midnight CDT, even if the web site says I can wait till midnight PDT.