Normally this value is determined from the payer master data.
Does the customer have invoice dates maintained in XD03 for the sales area?
For now I assume that none of the items is created with reference to a preceding document. If this is not the case, check the data in preceding document.
I also assume that your SAP version is not 4.7 or lower; if your system is really that old, I suppose that you have already reviewed the relevant SAP notes, so it makes no sense to remind you about them 
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Do you have by any chance some custom coding to fill VBKD?
This would be among the first things which I would check in this case.