The problem can be related to a registered hook in a module.
classes/stock/StockAvailable.php, line 619 executes this hook:
Hook::exec('actionUpdateQuantity', array( 'id_product' => $id_product, 'id_product_attribute' => $id_product_attribute, 'quantity' => $stock_available->quantity, ));
In my case, I had module "Mail alerts" enabled which uses that hook. Since my server wasn't configured to send mails, it was causing a huge bottleneck.
It was taking around 20 sec. on saving/deleting a product!
After disable the module it took 2 secs on PHP 5.6. I tested it on products with around 10 combinations each.