The active ingredient in most medicated starter is Amprolium. Corid is the common name for Amprolium.
http://www.corid.com/Pages/default.aspx . Giving more Amprolium is probably not the best course of action in this case.
Cocci is endemic in our environment. Pretty much all chicks will be exposed. You are technically right that medicated starter slows down cocci so that the chicks' body can handle it--but that's very far from "to minimize deaths." With healthy, non-stressed chicks, medicated starter does indeed prevent active cocci infection.
We still haven't determined if the OP does have cocci, and I don't think that they do, since only one chick died and the OP didn't say anything about severe diarrhea or other chicks looking visibly ill. Here is the technical breakdown on coccidiosis in poultry:
http://www.merckmanuals.com/vet/poultry/coccidiosis/overview_of_coccidiosis_in_poultry.html
We also haven't found out if the OP had their chicks vaccinated for coccidiosis. If so, treating with Corid or feeding medicated starter will nullify the protection from both the medicated feed and the vaccination.
If the OP was feeding medicated starter, and did actually get chicks with coccidiosis, then there is something else going on in the environment to stress the birds to cause them to not be able to fight off the cocci infection with the help of the medicated starter. Rather than throw more Amprolium at the problem, it would be better to find another coccidiostat just in case the cocci were resistant to Amprolium AND find out what the stressor is and eliminate it.
Personally, if the other chicks in the brooder are all acting healthy and happy, I would not treat them with medication they do not need. It's much more likely that there was simply something internally not right with that one chick. It happens.