In all my years as a shopper, not once have I ever seen an assignment on AA's website. Not even if I search every state. Granted I've never been on their website right at the release date they have listed. Do they really go that fast, or what?
I can always bring up a shop or two in my state or surrounding ones. Can you see shops that have been accepted by another shopper? The page is typically two fold: available on top, filled on the bottom.
I have never had this problem with them. There may not be anything available but the filled shops are still listed at the bottom with the option to apply as a backup.