Why does CiviMail stop sending after the first 1,000 messages?
Did you setup the cronjob?

http://wiki.civicrm.org/confluence/display/CRMDOC/Managing+Scheduled+Jobs

It's the usual behavior of civicrm to send 1000 mails per cronjob. After that it waits x Minutes and sends the next batch of mails at the next cron run.