By default notification lasts until the user interaction, you can make notifications sticky by enabling user interaction.

(This feature is available for Chrome 47 and above versions only. For the remaining browsers default notification duration is 20 seconds.)

Other than this while opting for scheduling notification you can not only send notification at desired time but you can set a notification expiry time.  

Note: If a user is not available online with the browser running, then the notification will be retired until expiration time. The maximum value is 28days.