Given the response of your Web Admin/Web Services, why not simply restart the daemon/services that get bogged down cyclically (e.g., once a day, once an hour) by some script. As you describe the situation, this should provide a workaround and has the advantage of needing only minimal effort.

Disclaimer: yes, this is not the professional way to do it. But if they don't want to diagnose ... how can you really fix the problem?

Christian Lemburg
Brainbench MVP for Perl
http://www.brainbench.com