This can be a very frustrating bug if you encounter it. This one happened to us, and it was very annoying because we didn’t realize some of our messages had not sent out until hours later when we wondered why the recipient hadn’t responded only to notice it was still sending.
What’s worse is that we never received the “Message failed” error, or the option to send it as a text message. This meant that we just typed out a message and hit send then went back to our business while the iPhone sat there “sending.”
The fix, luckily, is pretty easy. Usually, it just involves a simple reboot. That’s it. Turn off the iPhone’s power by holding the Sleep/Wake button until you see the the “Slide to power off” prompt. Then just slide it to turn the iPhone off. Hit the Sleep/Wake button again to power on.
Some users need to disable iMessages (Settings>Messages) and reset the iPhone’s network settings (Settings>General>Reset Network Settings). After that, turn on iMessage again.