Help I'm looking for a messaging app that will notify you without being closed

[surrealchereal]

This might sound weird, but I'm looking for a messaging app that doesn't have to be closed to notify you of a reply to your message. What I mean is, I send a message and then just leave the phone and when I get a reply the phone notifies me. It doesn't do that anymore, (I thought it did) I have to completely back out of my message program to get a reply notification. I have a Samsung Note 3 on ATT and I'm using the stock installed messaging program by Android.