Give clearing cookies and data another try. Make sure your Safari settings have Block Cookies set to Allow from Current Website Only. Restart the iPad.
To the best of my knowledge this site shouldn't be able to install adware (like it can do on other computers), only install a really annoying cookie. But it's possible it's getting re-installed almost immediately. The Block Cookie setting should help prevent that. Also, keep an eye on what site you visit and see if the problem re-occures for a particular site.
Good luck.