Actually, the fare expired at midnight, and I tried to book at 11:48 pm, CST. But I guess that the statement that the fare is good for "up to" 24 hours is waffle language that means that no fare is good, even if it is held.

In my case, I didn't book. I put the fare on hold, then tried to book before the expiration time. When I tried to buy it, I was given a fare of about double the original price. So, I called AA, got put on hold for about 25 minutes, and emailed AA before midnight, so I had documentation that I was trying to book before the expiration of the fare. Ultimately, I was hung up on (it was during those Dallas storms, and you couldn't get through to AA on the phone). I sent three followup emails when I had gotten no response. Now, about three weeks later, I got an apology for the delay and the statement I quoted above.

Obviously, since the fare has now expired three weeks ago, there is nothing that AA will do.