Magento did not release the Persistent Shopping Cart until Magento CE 22.214.171.124 so you shouldn't be able to see it in Magento CE 126.96.36.199. Attached is a screenshot of a clean install (with sample data) of Magento CE 188.8.131.52, it is not showing "Persistent Shopping Cart" under Customers.
Magento CE 184.108.40.206 Release Notes
If you can see it in another Magento CE 220.127.116.11, I am wondering if it is actually a CE 18.104.22.168 site, or a custom extension is doing it.
I would recommend first diffing both sites with a clean CE 22.214.171.124, and checking to see if core code has been changed, or if new core files has been added (like in the event of a failed upgrade to CE 1.6). Personally I use DiffMerge to do this, however there are several tools you can use.
Second, I would check what extensions are installed on each site and determine if any of them have to do with Persistent Cart.