I'm going to lose contact with my mother after I move out
Why would you want to lose contact with your mom?
I don't want to be a burden to my parents. They worked too hard for my upbringing and I want to give them a break.
Your parents invested a lot in you and have grown to love you. Cutting them off will be one of the most hurtful things you can do to a loving parent, so you should instead keep in contact with them.
Okay, I guess that is why I don't write home often.
I'm a little confused, as I can't tell if you want to cut off your parents or just feel you should. Either way, your parents clearly love you, since you say they worked hard to raise you, so you should stay in touch.