I found this reguarding worksheets...
It should still apply to your dropdown problem though.
Try "localising" your names to worksheets that are going to be copied.
So, if you have a worksheet called "Sheet1"
and a name MyName that refers to range Sheet1!$A$1
then delete MyName and then redefine it as
Note the "Sheet1!" prefix to the definition of the Name.
You may still run into problems if you use data validation that refers to
drop-down lists where the name of the list is localised to a different
worksheet, or conditional formatting where the "Fomula Is" refers to a named
range that is localised to another sheet.
Probably good practice to avoid duplicating global (not tied to sheet) names
and local names. It can cause confusion over which name is being called.
Jan Karel Pieterse's "Name Manager" is a useful add-in tool for clearing out
names that contain errors, identifying duplicate global/local names,
localising names that you have already defined as global and do not want to
go to the trouble of deleting first, and a whole host of other goodies