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Such problems are generally caused by javascript functions, I remember that your site is highly customized and with a long list of custom extension. To find this problematic extension I suggest to set your site under maintenance mode, and try to disable all extensions exept of those listed below, in such way you should be able to track this problematic extension. You can also try to download whole page on your hdd and create an copy of it on some dev domain, and there disable all extensions. You can also check that, this problem is not happening on fresh install of Jomsocial/Joomla or even our community/demo page.
Authentication - Joomla!
User - Joomla!
Azrul System Mambot For Joomla
jomsocial facebook connect
yes it's a pitty some extensions developpers can't be able to add that simple code :
if (!JFactory::getApplication()->get('jquery')) {
JFactory::getApplication()->set('jquery', true);