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This could be achieved using a workflow rule. I have done something similar for creating reference numbers for tasks. If all you need is the total number of times the 'due date' field has been updated, then a workflow running on 'is edited' for that field writing to a numeric custom field that could be used to increment each time the workflow rule runs.
I would be happy to show in more detail if you think it would provide the solution you need and you're not sure how to create yourself.