How to close this surface?

 From:  chippwalters
7128.1 
This seems fairly straightforward, but I'm having some problems closing this to a solid.
1. Sweep Rail
2. Sweep curve
3. Sweeped surface generated by 1 and 2
4. Planar top

And now I want to close the back (which you see is open). There are very tiny curves in the corner-- I've selected them and tried PLANAR on them and it works, but they cannot be joined to form a complete solid. Any idea why not OR how to fix?

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