Please see this thread in the W3 Total Cache Support Forum.
In addition to the OP issue which is NOT solved by implementing the recommended Woocommerce setting found here:
There is an IE issue described here:
In IE, if you remove a product from the cart, it is not possible to re-add that same product again unless you clear the IE web browser cache on the local machine.
So customers who add a product and then change their mind and remove the product but then later on come back to try again will not be able to re-add the product if using IE. That is a massive number of potential lost sales due to caching!
If you disable caching, the problem goes away.