SMS messages are not a guaranteed delivery service. Much like email, the messages are sent out over the network, and many factors can keep them from reaching the final destination. There is no guarantee that they will ever reach the desired destination, and they could be delayed by many different factors (like network nodes being down, nodes being overloaded and traffic being dropped, etc.).
People like to assume that SMS is guaranteed delivery, but it is not. Neither is email.
I have constantly had this issue. And it has caused major problems. As said before with receiving and NOT receiving text messages that are very time sensitive and impprtant. I am talking about lawyers, cases, and other seious situations. Why hasn't this been resolved? Clearly, it is after an "update" that my entire phone including text messages, internet, and just typing on the key board is a hassele. I have to reboot/master reset/factor rest/hard reset my phone multiple time's just to get it to work. It is not my phone itself but the software it tries to run. I am positive At&t customers are extremely tiresome of the generic at&t response to reset our phone, it is not user error. It is obviously something to do with in At&t server's and software updates. It seems to be getting worse.
I had the same problem occur. It took me about three days to figure out the root cause of the problem, but in the end, the solution was to delete all of my text history. I even tried moving my sim card between two phones without success. What I didn't realize that all of my text history was on both phones. Something to try if you're trying to troubleshoot this issue.