Your application is slow. You get a thread dump and look in the javacore and see lots of threads is ClassLoader.loadClass() with one thread holding the lock. You need to check your FFDC logs and look for "Too many open files." This means you haven't tuned the OS ulimit parameters and probably many others. Look in the InfoCenter for performance tuning and operating systems and pick the page for your OS. This should be the first link in the InfoCenter you access after you install WebSphere Application Server.
Edit: added link to the WAS v7 Infocenter page.