I'm not aware of any WWW::Mechanize limitation but I could be wrong. Most web servers will either choke inadvertently or throttle the concurrent connections to avoid going down. You're probably just hitting that limit in your tests.

To deal with this phenomenon, and to be a good network citizen, you should throttle your own requests to something reasonable, such as no more than three pages per second, or more kindly, one page per three seconds. Just call sleep(1) once in a while.