For many people, apps like Tasker, AutomateIt, or AutoMagic can add functionality. I think it likely that one of those apps can trigger a sound when a notification occurs
That's what I'm doing - using Tasker for repeating audible reminders for certain notifications. It gives me the flexibility that I don't think I would find in a purpose-built app.
I have levels of reminders setup - normal and priority. Each app/notification I monitor can trigger either level or reminder. Each of the following will trigger a reminder: missed calls, received texts, Gmail, Google Voice (voicemail), Hangouts, Calendar (I'm not actually using this right now), Google Now (reminders to leave for a calendar event - replaces calendar notifications). Any app that produces a notification can be monitored. Priority reminders occur every 2 minutes with a relatively obnoxious sound, for missed calls, unread texts, or received Hangouts messages from immediate family, or for Google Now reminders to leave for an appointment. All others result in a normal reminder - every 10 minutes with a more subdued sound. Priority reminders also go one level beyond my current sound settings, so if the phone is set to silent, priority reminders will vibrate, and if the phone is set to vibrate, priority reminders will make their normal sound.
I've also modified my setup to better work with my Moto X. Removing the phone from the holster (the assumption being that I'm checking Active Display) will cancel any active normal reminders, but priority reminders are only cleared by clearing the notification, viewing missed calls, or reading text messages. Additionally, when I'm driving (as detected by the Moto X), priority reminders for text messages are not set when the phone is not in the holster - the assumption being that they're being read aloud and responded to (the messages remain unread until opening the messaging app, but the reminders don't occur).
I'm also baffled by the absence of some basic form of repeating reminders in stock Android (even my flip phone supported this), but I seriously doubt that any stock implementation would have the features and flexibility of my home-grown solution - I'm really quite happy with it. The only thing I wish I could do (but can't) is to better integrate use of the Moto X contextual sensors to further control the reminder behavior.