jsvisit visitor counter is using its own ajax-request (it has no interface to other javascript frameworks)? What problem are you seeing? Do you have same issue if you disable the jsvisit module?
Cannot cooment on this as I do not understand your problem.
Checked your site's urls but cannot see any problem.
Also it looks a bit confusing to me, as plugin seems to be active on urls where module is displayed but inactive on all other urls of your site, where module is not displayed/used (This does not happen with jooomla 2.5 but seems to be a problem with joomla 3.x).
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