Why zombies don't eventually die in the walking dead?

We know the zombies live a fairly simple existence, they can only perform basic functions ( like walking ) and only care for eating flesh, cool. I understand. In the walking dead ( series ) literally years are passing since the first outbreak and these zombies are still alive. Wouldn't their brain eventually die due to low glucose levels or something? So even if the zombies are still alive years later, why so many of them? We know there are other groups constantly killing lots of zombies every day. Is this ever explained?