ItsSMC: Generally, yes.
It isn’t just “staleness”, but any process that takes food away from its original composition makes food less nutritious. It depends on the food as well, as things like fruits and vegetables rapidly lose their nutrition after they are cut or processed.
A lot of the healthy nutrients are “trapped”, in a sense, inside the less reactive environment that the food provides. There are molecules (enzymes) which interact inside fruit and vegetables which seek to preserve the health by various processes, such as bruising. Bruising, cutting, frying or anything else causes these responses, which changes that stable environment; consequently using the nutrition reserve.
Not all nutrients are lost this way, and it is usually specific to the vegetable, fruit, grain, or whatever. Some nutrients, such a minerals, can stay reasonably in-tact during these processes. Vitamins and proteins are often the first to go, as those are what the veggie/fruit/grain uses to protect itself, along with other organisms taking advantage of this “broken” environment.
When we look at why we taste as we do, it is to extract as much nutrients from our food as possible. Stale, rotting, or processed food are far down the path towards “unsustainability of their microenviroment”, or “potentially less nutritious” which is determined by our brain to not taste as good.
mr_panzer: Staling, at least as far as bread and bread like items are concerned, is just the act of water evaporating from the starch network. So the short answer is no. Unless you count water content as nutritionally important.