I was having some trouble the other day exporting a database that was about 40MB from Plesk's phpMyAdmin area and was getting a page could not be found error (though it appeared to work when only trying to export one table). This gave me the sense that it might be a memory issue for Plesk's PHP installation, and on searching I found a really good Parallels forum thread with exact instructions on what to modify. I found these instructions here: http://forum.parallels.com/showthread.php?t=81020

Open your plesk php.ini (my plesk php.ini located: /usr/local/psa/admin/conf/php.ini) 
Find memory_limit change to example: memory_limit = 256M 
Stop and start psa services: 
/etc/init.d/psa stopall
/etc/init.d/psa start