Is Never ending soup health implications a good question? As it is written now, it seems to be "Is never-ending soup unhealthy". Also, it doesn't seem to solve a problem that the OP is currently facing.
"Health" is a poor choice of wording but I think it's evident (to me, anyway) that it's essentially about bacteria and possibly other types of spoilage (rancidity?).
It could probably use some cleanup in terms of its tone and tempo, but it does seem like a legitimate question, particularly an extension of the one I linked to as related (Can one preserve food by periodically reheating it?)
The dialogue between myself and rfusca is further evidence that it's not pointlessly obvious; I'm generally a stickler for proper food safety practices but I probably would have thought of this as safe due to the constant re-cooking and high "turnover". Not that I want to debate the facts in this meta discussion, just that the question itself has some merit in that area.
Is it solving a real problem for the OP right now? Probably not. Is this something that could happen in the real world, possibly even in an (un)professional kitchen? Likely. It pertains to the common pasteurization vs. sterilization confusion and many less-experienced or simply less-safe cooks might decide that it's no different from reusing fry oil.
Again, I'd like to see some cleanup, but I think it should stay. My opinion anyway.