I own my car but it's older. I am VERY grateful that my parents are helping me up with maintenance. I am a grown adult but drive to school since it's way out in the booneys. I pay my own insurance, gas etc and have never asked for anything. When my brakes went I was prepared to leave it parked or take out a loan to get it fixed, and was overjoyed when my parents helped me out.
I don't think it's your responsibility but if you can afford to help out and don't think you are being taken advantage of them I'm sure it would be appreciated.