When you click “View Side by Side” in the "View" ribbon, Windows will arrange your workbooks one over the other, even if you had previously arranged them beside each other (“vertical” in Excel-speak). This is very annoying!
I solved this myself just as I was getting ready to post this message. It's almost embarrasingly easy, but not obvious. Still, it's annoying enough I thought it was worth posting in the forums.
The solution is to simply use “ViewàArrange AllàVertical” to get them back to your original arrangement after you've enabled "View Side by Side".
Hope this saves somebody time!