Marine Ich (Cryptocaryon irritans) is not a particularly lethal organism. It doesn't kill quickly.
The speed at which a fish succumbs to the disease is related to the health and strength of the fish; the kind of fish it is (and the kind of coating it has on its body); and the number of parasites the fish is exposed to. All things being average, a week to three would be expected.
It should be pointed out that the health of the fish doesn't prevent it from getting the disease. But if the fish has a lot of fat on reserve, it could give it a longer fight with the disease.