How long have you had the account and have you paid late in the past few months? If you always pay late, they will likely shut down your account in about 7 days. If you were always on time and this is the first time you were late, you will probably have about a month till they shut the account down. You will have a short time after that to pay the bill and have the account reinstated. Make sure you pay the bill, it gets higher and higher each month you ignore what is due and eventually you won't be able to pay it at all. it takes about 18 months before AT&T will allow a new account after that happens.
Like others have said, they get the message that the phone number is no longer in service. Service seems to be cut off around midnight or a few hours after, usually around the time the AT&T computers update.