There are a couple problems, at least these two, that happen when you duplicate a product. The specific prices and downloads(attachements) are not duplicated. They are supposed to be, if you look at the code in controllers/admin/AdminProductsController.php, via this block of code, and the associated functions in classes/Product.php..
if ($product->add()
&& Category::duplicateProductCategories($idProductOld, $product->id)
&& Product::duplicateSuppliers($idProductOld, $product->id)
&& ($combinationImages = Product::duplicateAttributes($idProductOld, $product->id)) !== false
&& GroupReduction::duplicateReduction($idProductOld, $product->id)
&& Product::duplicateAccessories($idProductOld, $product->id)
&& Product::duplicateFeatures($idProductOld, $product->id)
&& Product::duplicateSpecificPrices($idProductOld, $product->id)
&& Pack::duplicate($idProductOld, $product->id)
&& Product::duplicateCustomizationFields($idProductOld, $product->id)
&& Product::duplicateTags($idProductOld, $product->id)
&& Product::duplicateDownload($idProductOld, $product->id)
) {
...but they don't get duplicated.