Because, the body is dead. However, you're still alive. IMO, "living" is being controlled/manipulated. But the body is ca-put.
It looks like they heal, but at the normal rate (not Jack's previous accelerated rate).
It takes a while for a body to heal from castitrophic damage, and since it's only been a few days/weeks, even a simple broken bone won't be healed yet.
Rex appears to be healing...at least from the amount of the chest wound he showed to his dad, and the fact that he ran up the stairs rather than limped, like he was doing in the first episode. So, I would have to agree that people are healing at a normal rate, rather than their body being dead/non-healing.
Now, the suicide bomber who blew himself up (and then they detached his head), well...I don't think he'll be healing-up anytime soon...