iMessages Read Receipts Error - Will say Delivered until I send another message

I have a 64gb iPhone 6S running iOS 9.3.4, and I have had this particular device for about a month, but my previous 6S did the same thing.

The issue is when I send a message, it won't show a read receipt. It will only say Delivered. But when I send another message later, close out of the app, then open it again, the previous message will show a read receipt from a way earlier time. I've attached two images below as an example.

You'll notice the timestamp first; both these screenshots were taken in the same minute. In the first one, it says "Love you more" my message hasn't been read yet. But in the next image, after I've sent another message, a read receipt shows that it was read earlier that afternoon.

This is an error I notice primarily when texting my girlfriend simply because I text her most often, and because she has read receipts enabled (as do I). She has an iPhone 5. There isn't anybody else with read receipts enabled that I text often enough to notice this problem. And it isn't entirely consistent. When she and I are texting back and forth immediately, the read receipts function normally.

I was just wondering if anybody else has experienced this problem and if there's anything else I can do to fix it.