Thanks for sending me in the right direction.  I got it to work by putting 2
new commands in the "SplitMergeLetter" macro I copied from Graham Mayor's web
site.  The first command unprotects the new document and the second command
re-protects it.  I'm copying it here in case anyone in the future (who feels
WAY in over their heads) needs it:

Sub Splitter()
ActiveDocument.Unprotect
Selection.EndKey Unit:=wdStory
Letters = Selection.Information(wdActiveEndSectionNumber)
Selection.HomeKey Unit:=wdStory
Counter = 1
While Counter < Letters
Application.ScreenUpdating = False
With Selection
.HomeKey Unit:=wdStory
.EndKey Unit:=wdLine, Extend:=wdExtend
.MoveLeft Unit:=wdCharacter, Count:=1, Extend:=wdExtend
End With
sName = Selection
Docname = "c:\in process\merge\" & sName & ".doc"
ActiveDocument.Sections.First.Range.Cut
Documents.Add
With Selection
.Paste
.HomeKey Unit:=wdStory
.MoveDown Unit:=wdLine, Count:=1, Extend:=wdExtend
.Delete
End With
ActiveDocument.Protect wdAllowOnlyFormFields, NoReset
ActiveDocument.SaveAs FileName:=Docname, _
FileFormat:=wdFormatDocument
ActiveWindow.Close
Counter = Counter + 1
Application.ScreenUpdating = True
Wend

End Sub

FYI: You need to change the Doc Name to a valid path and make sure the file
name is the VERY FIRST thing in the document