What I've found for years, is if you cross 'x' number of searches, and then try to log in, you'll get some variation of these errors. Especially if cycling international city pair searches that aa doesn't fly direct to. 'X' seems to vary quite a bit.

When I'm done searching and ready to book, I'll close and exit the browser I've been searching on (browser is set to clear cookies on close), and use a different browser to log on and book. A browser that I rarely use for searches, until I'm ready to book. 90% of the time this process works for me.