Can you please post a link to the page so I can see the behavior?
This type of issue is usually related to PHP session not working on your site. A quick way to find this out is to add a product to the cart then browse to different pages of your site. If the session isn’t working then the Cart will get emptied out as you browse to other pages since the value gets lost.
If this is the case then your hosting provider should be able to fix your PHP session issue… it’s usually a matter of adding a line to your PHP.ini file on your server.