Changing Simple product to External/Affiliate product

I have been selling some products, and I wish to change them from Simple products to External/Affiliate products.

The Simple products have been Out Of Stock.

However, when I change the Product Type to External/Affiliate, it is not showing in the product listing on the front end.

If I create a brand new External/Affiliate product, and configure all of the properties which are visible for an External/Affiliate product to be identical to the visible properties on the existing/converted product, the newly added one shows as expected in the product listing on the front end.

Is there something I need to do when changing the product type to ensure that they are visible? I do not wish to create new products, as I have links and sales history of the old products – I wish to maintain the existing product listing, but simply change it from a Simple to an External/Affiliate.

Thanks.