In case anyone else comes across this problem, I found a solution -
activating the sheet containing the range to be published:

Private Sub ExportHTML(ByVal dateEffective As Date)
Dim objPubOb As PublishObject
Dim strDate As String

strDate = Format$(dateEffective, "ddmmyy")

For Each objPubOb In ThisWorkbook.PublishObjects
With objPubOb
If .SourceType = xlSourceRange Then
.HtmlType = xlHtmlStatic
.Filename = Left(.Filename, Len(.Filename) - 10) & strDate &
".htm"
ThisWorkbook.Names(.Source).RefersToRange.Parent.A ctivate

.Publish (True)
End If

End With

Next objPubOb

End Sub