ok, here's my take on the subject: Living things all share the property of local action against entropy. That is to say, within a living thing there is much more order than you would find in a random distribution of compounds from the earth's crust, or in a distribution of basic organic building blocks. Essentially, these pieces (amino acids, sugar molecules, nucleotides, etc.) are arranged in specific patterns. More than that, though, is the fact that they continuously work against entropy. If all the chemical machinery in a cell stops working, it's not long before the component molecules begin to decay. Some have longer life-spans than others, and some are actively disassembled by specific proteins, but without a supply of replacement parts being made, the cell will die. (this is similar to what others have already said about homeostasis)
Death, then, is the point where the organism isn't able to start back up again and repair itself after some block is inserted/removed, or injury sustained. If a bacteria is physically sliced open, cut in two, it won't be able to repair the damage quickly enough and will lose its self-sustaining capability as its contents spill out into the surrounding medium. If you instead deprive it of all food, or just a certain specific nutrient, it will be unable to reproduce but will still survive for a while. It must be considered dead at the point where it has decayed internally so much that even with the addition of food it is not able to revive. With a person or other multicellular organism, this window is pretty short because of the interdependence and complexity of the body. If your heart stops on the operating table, the doctors have mere minutes to revive you before too many cells die and you are beyond recovery.
