This error can be due to the fact the user has recently completed a removal order for the item so he was not eligible to send it in again.
Another possible reason for the ITEM_INELIGIBLE may be pricing error in Seller Central per case: https://inventorylab.zendesk.com/agent/tickets/17329
To fix this, have them to go SC and navigate to Pricing>Fix Price Alerts:
If the item is not shown in the Price Alerts, then check to see if it is in stranded inventory and there will be instructions there on how to fix them:
If it is not listed in Stranded Inventory, have the user select that item from the Manage inventory page and then Send/Replenish under the Action button. This should generate the error message when attempting to add to a shipment and can then fix or contact Seller Central Support.