I update me prestashop store many times so today I find in my database this:
UNIQUE KEY `id_product_2` (`id_product`,`id_shop`,`id_shop_group`,`id_currency`,`id_country`,`id_group`,`id_customer`,`id_product_attribute`,`from_quantity`,`from`,`to`),
And when I update-save_new product I have mesql error "duplicate KEY `id_product_2` ...." (only when active debug mode).
In fresh install prestashop 1.5.4.1 we dont have UNIQUE KEY `id_product_2` so we dont have error but we have duplicating product in "ps_specific_price" who have specific price from "ps_specific_price_rule".
Now I am sure store slow only when update-save_new product. Now when I truncate "ps_specific_price_rule" saving-new and updating product little faster.