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If you change the document after signing, it will invalidate the signature.
By default a signature will lock all the fields, you will need to uncheck the 'Lock the fields after signing' checkbox in the properties tab to change a field.
The other option is to put your code for the date in the PreSign event for the signature object, that way you will update the field before signing but will be still valid and locked after signing.
this.resolveNode("DateTimeField1").rawValue = util.printd("yyyy-mm-dd", new Date());