We don't add nutrients during primary or secondary fermentation for several reasons. For purely philosophical reasons, we believe that one of the best ways to have the wine speak of the vineyard is not to add anything (our exception is SO2 but that might change). For practical reasons, we never learned how one handles nutrient additions since we trained under Eric Texier who shares our philosophy.

As we have learned more about world of additions (course work and industry seminars), we have also added a third reason, we aren't sure what it will help grow. Brettanomyces, for example, is a yeast which can thrive off nutrients which the Saccaraomyci don't devour. Adding those nutrients has always seemed counter intuitive. (If fact, it is often hard to keep Brett alive in the lab and for beer makers who want to utilize them for Lambics. Recipes for the agar, media which the Brett grows on, often include something rich in micro nutrients. See http://brettanomyces.blogspot.com/ for what looks like an easy recipe. Key growth nutrients are found in yeast extract and commercial yeast nutrients. )

Vitamins for humans may promote unwanted growths as well. The New York Times recently published a fascinating article on vitamins and their proven impact both beneficial and otherwise.

But some vitamin studies have also shown unexpected harm, like higher lung cancer rates in two studies of beta carotene use. Another study suggested a higher risk of precancerous polyps among users of folic acid compared with those in a placebo group.
Tara Parker-Pope - http://www.nytimes.com/2009/02/17/health/17well.html

The article made me think that what we do (or in this case, don't do) for our wines perhaps is a reasonable choice of us as well.