It is advisable to feed prekilled or stunned rodents, as there is a slight possibility of damage from the prey during the kill. If you feed live prey, be sure not to leave the snake unattended. If the snake refuses the rodent for any reason, remove it and offer it on another day. If your snake unexpectedly refuses food, consult a professional for advice. Do not repeatedly offer what it does not want to eat as the snake may become conditioned to not want that prey item in the future and you may be wasting valuable time in correcting potential health problems.
Corn snakes can fast for long periods, but only if they have to.
I recommend that you establish a routine feeding schedule. You don't have to adhere to it strictly, but long periods of fasting are not recommended unless you are brumating your snake in preparation for breeding under proper temperature conditions. Consult a breeder or a good corn snake book if and when you are ready to breed your snake. Remember, after the offspring hatch they are an enormous responsibility and if you don't know what you will do with the babies, don't breed the adults. Enjoy your corn snake.