Two MovieClip instances with the same name..?

Hi All,
The zipped attachment for this post, contains two files trial.fla and img.jpg.
In the flash movie, I have done the following:
Created three frames with stop() on all the three.
“Prev Frame” & “Next Frame” buttons allow us to move to all the three frames.
There is a movieclip instance with the name: “abc” common to all the three frames.
The button “Show/Hide Abc” makes “abc” visible & invisible.
In the second frame, I am loading the external image “img.jpg” and setting the child index of “abc” to numChildren - 1.
Now if I move to frame 3 and try to hide “abc” (using “Show/Hide Abc”), it works fine. But once I switch back to frame 2 or subsequently to frame 1, I can see two instances named “abc” in the trace window. (I display all the children of the displayList on every frame). **Why do two instances named “abc” appear?
** Due to two instances of “abc”, the button to hide “abc” no longer works.
Can you help me fix this? Its very important.
NOTE: If I do not change the childIndex of “abc” to numChildren - 1 then everything works fine. But I have to do this in my project where a similar problem has crept up.