Currently the only way to save a design is to either click “Save & Exit” within the product customizer or to fully add a product to your cart. Please make sure that you are clicking the ‘Save & Exit’ tab while you’re in the customizer or checking out with a product, otherwise our system will not save the design you’re working on.
We are aware of this issue, and we are currently working on a solution that will automatically save your customizations to your Saved Designs section (as long as you are logged in). In addition, we will also be adding a "Save & Continue Later" button to the Preview & Add to Cart (where you review your proofs) page as well. But for now, you will need to either fully check out with a product, or save it within the customizer.