Are you using Magento version 1.9.x for your store and order email confirmation not being sending? Don’t worry be patient, it is not a bug. You can easily fix by below process.
Starting with Magento 1.9.1 the emails are not being sent directly during place order but instead are being queued. The queue is being processed via your Magento Cron job. Please double check this has been configured and is running correctly.
Popular cronjob checking extension AOE_Scheduler / Cron Doctor can help you in confirming that your Magento cronjob has been configured correctly and is running.
Hope it will help you. Best of luck!
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