I have a problem with my Imessages showing that they are delivered, then read, then going back to showing that they are delivered. And also, my messages show they are delivered and not read when I know for a fact that person I sent the message to, saw my text.
If the person you sent them to doesn't have their phone set to send you a read report you won't get one. Example, no one that texts me on my iPhone will get a read report because I have that option off in settings.
Settings / Messages - Send Read Receipts is the setting that controls whether a "read" message is sent. I leave mine off since I really do not want people knowing exactly when I am reading their messages. But if you want, go to Settings / Messages and turn it on.
Besides the fact that "read receipts" is a setting set by the recipient, not you, you may not get what you want.
Furthermore, if the entire message can be read in the notification window and the recipient does not have to go into the iMessage app in order to read the message, THAT is why they may have read it while it not being marked as being read by the recipient. It is only marked as being read when they open up the message thread in the iMessage app. If they have seen the entire message in the preview window in the notification screen, they may not see a need to go into the iMessage app to look at the message again.