I was doing some research on this myself and from what I had found, the body has hox genes that direct the formation of body parts. So now the obvious question is that if a body part contains stem cells and hox genes, shouldn't it be able to regenerate a new body? Well, perhaps. But the problem is that as organisms become more complex, the process of the creation of their bodies also becomes more complex. For example, in the fruitfly, if the labial gene function is not expressed, the mouth and head that develop outside the body do not get involuted and that prevents the salivary gland from forming.
So the answer about why multicellular organisms can't regenerate so easily simply seems to be because the process of creating a multicellular body has for some reason become an extremely complex, intertwined process where various body parts creation is dependent on other body parts creation. So in the evolutionary process it's entirely possible that the stem cells noted that there's no point trying to regenerate a body part, and therefore they just don't.
Here's an anomaly. There's a jellyfish that can reverse aging and go back to infant stage. I think it's able to do so because it has a simple body structure.