What is the zombie lifespan? If we can figure out how long zombies survive, we have a lot better chance of surviving ourselves. Unfortunately, we're never going to be able to pin it down exactly, but what we can do, because we know that zombies occupy the human body, we can look at the stages of human decomposition.
What we learn is that human goes through 4 distinct stages of decomposition: The first one being the Fresh stage. By the end of the Fresh stage of decomposition, the bacteria in our mouths has eaten out our brain so much that it oozes out of our nose like yogurt.
If zombies are powered by their brains, their heart's not beating. What makes them undead is that their brain is what's driving their processes; it stands to reason that they would not survive beyond the Fresh stage of decay. That may be much longer in a zombie then it is in a normal decomposing body, but in theory zombies, would not last beyond the Fresh stage of decay. The Fresh stage of decay in humans varies on climate and conditions of the body, but it can be anywhere between a week to several weeks.
Humans decay because the bacteria that's naturally occurring inside our body takes over once we're dead, and essentially eats us from the inside out. If zombies are able to suppress this bacterial activity, then it stands to reason that they would survive much longer than a naturally-decaying human body.