Error 21916583: Variation is required for a listing that previously had variations

When I make this ReviseInventoryStatus call:

<?xml version="1.0" encoding="utf-8"?>
<ReviseInventoryStatusRequest xmlns="urn:ebay:apis:eBLBaseComponents">
<InventoryStatus>
<ItemID>110040029410</ItemID>
<Quantity>0</Quantity>
</InventoryStatus>
<RequesterCredentials>
<eBayAuthToken>*****</eBayAuthToken>
</RequesterCredentials>
</ReviseInventoryStatusRequest>

I get the following error:

ShortMessage:  Variation is required.
LongMessage:  Variation is required for a listing that previously had variations
ErrorCode:  21916583
SeverityCode:  Error

Summary 

The Quantity of an item cannot be set to zero.  If you need to set it to zero because of out of stock situations, then the alternate is to end the item and relist it when quantities become available.  The ReviseItem family of calls will return an error if you set the Quantity to zero.

Additional Information
ReviseInventoryStatus

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