Have reviewed your install and you're trying to load 2 PHP extensions that don't exist in the extension_dir you specified. I've disabled the following in your php.ini and it's now working fine. Please also confirm is working fine.

extension=magickwand.so
extension=imagick.so

When an extension doesn't exist the server throws an error and it kills other processes. Those 2 simply didn't exist so it messed up ioncube loading and functioning properly, but they only loaded in select locations when called (phpinfo, probably CB config, etc..).

Your host should've easily seen this in their server error logs; this also would've slowed down your site a good bit. Another possibility is the two exist, but are compiled wrong or wrong versions and not working.

Simple test was to supply a php.ini file with only ioncube in it to rule out php.ini settings conflicts.