Most web hosts will suspend your web hosting account if you start sending out 20,000+ emails everyday. This number is just an example. Every web host will have a different threshold but the the number is typically less than 20,000 emails per day. When a web hosting customer starts sending out thousands of emails everyday. The web host may think you are spamming people.
Web hosts typically apply a limit on the number of emails that may be sent out every 60 minutes (per hour). The rate is typically less than 1,000 emails per hour. If you want to increase this rate you will have to contact your web host. Your web host may have you move over to an email plan to accommodate your account needs.