I am trying to import products using a custom made import profile. Here I set some values on the product and then save it, like this:

$product = Mage::getModel('catalog/product');
$data = array();
// Inbetween I fill $data with some values
$product->addData($data);
$product->save();

However, the products do show up in the admin, but do not show up on the frontend (I did add them to categories).

The odd thing is, they do appear on the frontend once I open them in the admin and save them again (without modifying anything). Am I forgetting something, or some value that is somehow set by that action?

I tried to rebuild all indices in the backend and to clear the cache, but this does not work, contrary to Magento API: Rebuild Indexes after adding new products.