Replicators are based on transporters, which can operate in two modes: molecular and quantum. The molecular level allows you to replicate most nonliving objects, while quantum level resolution is required to keep a living subject's neural patterns intact during transport.
Molecular-level transporter patterns are relatively small, at least by 24th century standards. They can be stored rather easily, and in fact the replicator has something called a "pattern generator" that builds patterns based on, say, a recipe for roast chicken and its knowledge of a chicken's genome. However, quantum level patterns are enormous; they can only be stored in temporary memory that degrades within about 90 seconds. As an example of this, in the DS9 episode "Our Man Bashir", they had to store the quantum-level patterns of a few crew members in long-term memory for a few hours, and it involved wiping essentially every other bit of memory on the station to make room for them.
As such, it's only feasible for a replicator to work on the molecular level. A quantum-level pattern would be way too big for it to store or generate. Thus, it cannot replicate a living being (sentient or nonsentient). It can create a dead body in all its glory, but not even the smallest actual living microbe.
I think they called it "a spark of life that can not be replicated".
Kitface 19:27, June 29, 2011 (UTC) : Of course, in the future (like 25th century or more), it will probably be feasible to store quantum-level patterns quite easily. But then there are ethics of generating alive things to eat (it would probably get more use from the Klingons - there's noting worse than half-dead racht, after all!