Ignoring for the moment the entire question of how a replicator would work in the real world (this is fiction after all), the problem with latinum not being replicable is non-trivial.
We have been told that replicators can't handle some kinds of radioactive materials - which makes a kind of sense since the material being replicated would changing continuously - except that's an argument for why some materials can't be transported. It would also mean that latinum is constantly decaying into something else - and that would make it a terrible form of currency.
The whole problem stems from a core problem with ST science - the writers don't seem to fully grasp what's an element, a chemical, a subatomic particle and so on (don't get me started on that horrifying stupid 'omega particle' rubbish introduced in Voyager - or worse, 'red matter' in the first new ST movie... A chemical way to create black holes? Really?).
Latinum seems to be an element (like gold). In fact, it kind of has to be by reduction: if it's a chemical, it's made of elements and we're back to elements (same argument for alloys or amalgams). That implies then that there's a non-radioactive element that's not replicable.
Thing is - no matter how complex (which can only mean 'large') an atom gets, it's going to operate on the principles of quantum mechanics which are predictable. Any process which can take energy and essentially squeeze it into electrons and quarks and then glue quarks together to make protons and neutrons is already going to have more than enough power and precision to make any atom, no matter how complex.
Sooooo... neilfien@neilfien's answer is basically dead on, and BBlake@BBlake's answer has the reason.
Jeff's@Jeff's answer while technically correct is putting the cart before the horse and isn't so much answering the question as justifying it. :)
