This is something I do not understand with java as a webserver - doesn't such behavior show a major design problem?

"Lots of traffic" can be expected by any webserver software - handling "too much" of it in a not too painful way could be a design goal. Just spitting out an error on such a condition and making the site disappear is a little bit too simplistic for my taste.

I have seen this error on sites with java webservers many times - is this an accepted limitation in the java world?

I am not trying to be snarky here, I have lots of respect for aphyrs work, but I am really wondering about this "normal behaviour" of java webservers - how can an "enterprise platform" get away with this?