Am I sinful or accountable if the owner of money in my possession refuses to pay zakat on it after a year has passed and I have reminded him of its obligation?

Since you have advised the owner of the wealth, you have fulfilled your duty. There is no sin upon you if he refrains from paying zakat, but do not assist him in keeping the amount of zakat due, because zakat is tied to the wealth itself, not to the owner's liability.