That's a design/ideology conflict and not something that can be fixed. On OS X, you can leave a webpage open, and it must be open in order for the notifications

That's a design/ideology conflict and not something that can be fixed. On OS X, you can leave a webpage open, and it must be open in order for the notifications to be sent. On iOS, you cannot (terminated whenever there is memory pressure). Push notifications are just way beyond what a website should be able to do, and scheduled ones aren't really all that useful except for a handful of apps.