It happens to me at all times of day. I'm pretty sure it's some sort of DNS issue, because when I switch to Google's DNS servers, the problem goes away. When I use my ISP's servers, I can randomly not get into AA at basically any time of day. But it's not a one-time problem; this has been an off and on thing with AA for *years* with me. It's the only web site I ever have this problem with, but it's caused me to switch my DNS over to Google. I'm not sure what it is but the fact that it happens with my ISP's DNS servers but not Google's suggests that I would not be the only one having this issue.
That said, I don't have any idea where the fault lies. Sometimes these kinds of things are caused by a small misconfiguration that one DNS server will ignore while another will freak out over, or at least cause problems if there are other minor issues on the network.
But I would suggest to anyone else to just switch to Google's servers in your own network config... their DNS servers are 188.8.131.52 and 184.108.40.206, and they're open to the public (and they're reliable).