Ich medication can only kill the ich parasite while it is in the free swimming stage of its life cycle. Depending on water temperature this freeswimming stage can be between a few days and a few months after the ich is visibly infecting your fish. Essentially while infected your fish will either recover or not, the medication is doing nothing to help your fish.
This is why increasing water temperature is important to ich treatment. This will increase the rate at which the ich parasite goes through its lifecycle. If you get the water temp up to 86f (30c) the ich parasite takes about 1 week to go through its whole lifecycle and the medication has a chance of killing off the parasite during the freeswimming stage its lifecycle if you medicate for a few days after you no longer see signs on your fish. It should tell you this on your ich medication. At cold water the life cycle takes a couple of months and so your medication wont still be in the tank during the free swimming stage (unless you continue to medicate for months) and you run the risk of reinfection. Tropical water temps the life cycle will probably be a few weeks, so at this temperature i would continue to medicate for at least a week, but thats a guesstimate. Plenty of gravel vacs after the parasite drops off your fish to get the parasites out of your substrate too.
Healthy fish with a good immune system will typically live with ich just fine and show no signs of it. This is why it can suddenly appear for no apparent reason. If a fishes immune system gets compromised, ich thats been in the tank for years, can suddenly take advantage.