Hello Milan_VC,
Welcome to AbanteCart forum.
What you describe is a correct behavior. Customer's active cart is stored in the session and specific to given session. Once the session is lost or customer is logged off, sessions is cleared.
With new login, last cart content will be loaded from the database.
To achieve you requirement, you will need to reload cart from database all the time.
This code is in the customer class
https://github.com/abantecart/abantecart-src/blob/master/public_html/core/lib/customer.php#L191