It's because the description of the product is changed dynamically when you change a characteristic. And since the JS code of the tabs of your plugin is not dynamic, the tabs don't work once copied.
The fix is quite simple, just edit the file "show" of the view "product" via the menu Display->Views and remove the code:
<div id="hikashop_product_description_<?php echo $variant_name;?>" style="display:none;">
<?php echo JHTML::_('content.prepare',preg_replace('#<hr *id="system-readmore" */>#i','',$variant->product_description));?>
</div>
That will remove the update of the description when the characteristics are changed and thus avoid that problem.