I'm deciding on if I should buy an xbox 360 but the live memberships cost a lot. If I don't use my xbox at all on a certain day, will a day still be gone from my live membership?
The Xbox live membership expires on a certain day always. No matter if you are using your Xbox or not.
Furthermore the membership will be refreshed automatically, if you do not unsubscribe or cancel the automatic refreshing.
One more hint, if the membership is very pricey for you, consider to options: Only get a one month subscription, when you really know you will play enough. Or you can buy a full or half year to get a discount.