Safari: The prompt is modal, and will be shown exactly once. If the user disallows notifications, then they must go into Safari->Preferences->Notifications and change the settings to enable notifications. Whatever they choose, the user will never be prompted again, unless they remove the subscription from the notification list entirely.
Chrome: The prompt has three choices: Allow, Disallow, and Dismiss (x). If the user selects Allow or Disallow, then the choice is permanent, and no further prompts will be shown for that site. If the permission dialog is dismissed or ignored, you can re-prompt the user on subsequent page views.