go to staging.acinolilla.com/shop and select 3 products to compare.
Now go to the compare page. Only 2 products are displayed, not 3.
Now click on the remove button. You cannot remove all 3, and when you try to remove the last one, a new one appears on the page … at least this is what happened on my side …
Please deactivate all the 3rd party plugins and activate only theme-required plugins on the site and then check the issue. I am sure your issue will be solved. Then Activate the 3rd party plugins one by one and check which plugin is creating the issue for you.
Otherwise, if the issue still exists then keep the 3rd party plugins deactivated and share the wp logins details i will check and give you a possible solution.