I've used as user many other panels in the past, and i can say that in cPanel and Plesk the problem doesn't exists.
I use a lot of wordpress installs on my servers and I can say you that I never had this problem on any ispconfig server. So this problem is not related to the use of ispconfig.
Which PHP mode have you used for the website? CMS systems like wordpress require php-fcgi and suexec must be switched on in the site settings. Beside that, make sure that the files and folders in the web directory are owned by the web user and client group of this website.