Explanation
The most likely cause of why some orders were missing from the Data Loader export is that the Status was still set to Draft. The Status is a field on the Order Summary object that indicates the current state of theorder.
The Status can have values such as Draft, Submitted, Confirmed, or Cancelled. A Draft order is an order that has not been submitted or confirmed by the customer or the seller. A Draft order is not considered a completed or valid order and is not included in reports or exports. When using Data Loader to export data from an org, Data Loader will only include orders that have a Status other than Draft, such as Submitted or Confirmed. If an order has a Status of Draft, Data Loader will not include it in the CSV file, which may result in missing orders.
The export job did not fully complete is not a likely cause of why some orders were missing from the Data Loader export, as it is not related to the order status or data filtering. Order Life Cycle Type was Managed is not a likely cause either, as it is not related to the order status or data filtering. The Order Life Cycle Type is a field on the Order Summary object that indicates whether the order is managed by Salesforce Order Management or by an external system. The user does not have rights to some of the records is not a likely cause either, as it contradicts the fact that some orders were exported successfully. If the user did not have rights to some of the records, Data Loader would not be able to access or export any orders at all. Salesforce References: B2B Commerce Developer Guide: Order Summary Object, B2B Commerce Developer Guide:
Order Status Enum, Data Loader Guide: Export Data from Salesforce