I too was struggling with NBS (Non-Breaking-Space) and Word 2013. I am working on a document with Sanskrit 2003 font. I thought the issues were font related, because my NBS in English text, in the same .docx works properly. Remembering that NBS worked in a file I had earlier proof-read, I tried several tricks such as copying the format from the older file etc.
This worked and didn't - as the font size was changed, NBS would work in some places, and not in others!! (All related to Sanskrit 2003).
Then I tried saving the file I am working on now, to .doc format. Hey presto! IT WORKS! SO much for Word 2013!!
Hope it works for you too!