Drop down menu with protected sheet

I need your help.
I have a little file Excel.
This file has protected sheets with drop down menu and these are the steps:


1)double click to show Userform1;
2)click on CommandButton of the Userform to write on the protected sheet:
Private Sub CommandButton1_Click()
ActiveSheet.Unprotect Password:="password"

Range("a1") = "prova"

ActiveSheet.Protect Password:="password", DrawingObjects:=True

Unload Me
End Sub



The problem is that when I fix manually protected sheets, double click on cells with drop down menu does work, but after I execute the "Private Sub CommandButton1_Click()" procedure, drop down menu doesn't work any more.
Is it possible to force drop down menu to work also after I execute the procedure triggered by CommandButton1?
I need Userform1 to show after double-click event, also for the cells formatted with the drop down menu.


Thank you in advance


I tried changing parameters of the Protect Method, but with the same result.