There are few possibilities that order status is not changing.
1.You have made some modifications in Auctane Shipstation Shipment Model file app/code/community/Auctane/Api/Model/Action/Shipnotify.php.
Try to use fresh shipstation extension.
2.Your Magento 2 store is in maintainance mode or sometimes in production mode it breaks, try to test in developer mode.
3.Check any extension you recently installed having these events: sales_order_shipment_save_after or sales_order_shipment_track_save_after
Disable these events from etc/di.xml or simple disable those extensions.
4.Check var/exception.log and find recent exception related to shipment.
FYI - shipping cost and rates do not save in magento by shipstation.
you can only view , shipping carrier and tracking number in magento orders.
Also there is a feature that prevents ShipStation from updating a marketplace that an order has been “Shipped”. You can create an Automation Rule to apply this setting to your orders that import by going to Account Settings > Automation Rules > Create a Rule > Only apply this rule to orders that match a specific criteria > choose your Magento store > Add an Action > select Do Not Notify Marketplace from the dropdown menu > Save Changes.
Still , if you face issue you may open support case on shipstation.