I'm on aa 732 departing dfw-lga at 12:20 pm. [I was searching to see how many f seats were available].
If I set the time for flights after 7:00 am, 732 is NOT listed (though earlier and later (than 12:20 pm) ones are.]
If I set time to 11:00 am, 732 IS listed.

We just did an Award search and see AA 732 without issue using the default 12AM search time. Since you didn't mention which award class you were searching for, or post the results, we can't replicate whatever it was you were seeing. However it sounds like the flights didn't show because there was no award availability on several of them today. As we note in the help for the Award search results page, and has been posted in this thread before:
Sometimes American will return just two flights where the requested award seat availability is zero on both flights, even when there are later non-stop/direct flights scheduled. This is American's way of indicating that none of the later flights have available inventory for the request class either.
If you have a question about a specific search in the future please email us at
[email protected] so we can help you faster, thanks.