Is there a way to keep notifications active until I resolve them? (Moto X 2nd Gen)

[AC Question]

On my previous phone, I would continue to get the LED notification and status bar icon until I had actually visited and dealt with whatever the notification was about. I would also get a status bar icon until resolved.

With the Moto X 2nd Gen, I get an audible notification and the Active Screen shows the icon for the type, but if I neglect it....it simply goes away after 15 minutes or so.

Thus, if I have a reminder to call 'Jane' at 2pm but I don't act on the Active Screen notification and reset the reminder for later....it just goes away and I have no further reminder that I missed a call, etc.

Is there a setting I'm missing that will keep a notification on either Active Screen or status bar icon (text, email, calendar reminder, etc) until I delete it, act on it or change it?

Thanks!!