David, does the default "flatten fields" key Ctrl+6 work for you? As far as I am aware, this should work with any field.
I can't check until after the weekend (all my interesting files are at the office), but I'm pretty sure the private Endnote data gets kicked out after a Flatten Fields command, because I have had the OP's problem in the past but can't remember encountering it after I started to rigorously Cleanse Word files.