When I am at the checkout page for my shop, I see the quantity is set to 1 for a product that I just added to my cart. When I try to change the value to another number and click update quantity, it still stays at 1.

The reason this is happening is because you have set the default quantity for this product to 1. This means a user can only purchase one of this product per order. If you would like your customer to be able to purchase more then one of this product, open your shop in Shopping Cart Creator and select the product you wish to change. Next, click the More Options tab. At the bottom of the tab under the Quantities section, change the option from Use Default Quantity to Buyer Choose Quantity.

Note: If you have only a limited quantity of this product, make sure to monitor your sales so you do not oversell it.