We believe that on your website you might be using the Ajax add to cart method for adding the product to the cart. In some Ajax call, they are not collecting all the fields added in the add to cart form, they only pick the product ID and Quantity. This might be the reason why the extra product options are not showing on the cart page.
Could you please verify whether you are using Ajax add to cart method, if so please turn off the Ajax method for adding the product to the cart and verify from your side.
We hope this will help.
Thank you!