Brian here from the Shopify support team.
You can let your customers buy your products when they are out of stock. You just need to choose the correct settings enabled on all of your products, and to track the inventory of each product.
Many of your products inventory is N/A (not available), which means the inventory is not being tracked. Take the "Isla dress" for example. This products inventory is N/A, so this is what you need to do - http://take.ms/h666d.
Once you follow those instructions, you will see that customers can purchase your out of stock items.
I hope this helps you out :)