Commerce: Modify the order price
If I understand it correctly, a shopping cart refresh causes the recalculation of your line item price(s). For documentation on this topic, see sell price calculation on drupalcommerce.org and the referenced Prezi presentation on that page.

Maybe you can adjust the price calculation, by adding pricing rules that react on the event 'Calculating the sell price of a product' and use the action 'Set the unit price to a specific amount'.

Otherwise, you could implement one of the hooks provided by commerce_product_pricing.api.php.