updated 01:29 am EDT, Tue October 1, 2013
Not affecting all users, but restart appears to clear up the issue
After upgrading to iOS 7, some users are finding that the Messages app doesn't reliably send out texts as a fallback when an iMessage can't be sent, and in some cases doesn't reliably send or receive iMessages. While the problem was first reported when iOS went live, reports have increased as hesitant users capitulated upon the release of v7.0.2. A simple fix usually just involving rebooting the device appears to work for most, but a slightly more elaborate fix seems to cure the issue permanently.
The problem could stem from users' habits of rarely (if ever) actually powering down or resetting their mobile devices ahead of downloading the upgrade. The reliability factor on iOS is even higher than that of OS X, and consequently some users almost never actually power down their iPhones, iPod touch or iPad unless the battery goes dead or a new software update forces a restart.
For many users reporting the iMessage issue to Apple's Support Communities, simple powering down and restarting or resetting the device appears to have fixed the problem. For others, it was necessary to temporarily disable iMessages, reset the iPhone's Network Settings, and then re-enable iMessage. The latter method was confirmed by an AppleInsider staffer who suffered the issue. A simple restart will usually also re-establish network settings with a carrier or Wi-Fi provider.
For such a significant system update, the transition to iOS 7 has gone largely swiftly and with only a few relatively minor issues. The iPhone continues to suffer some bugs in its handling of emergency calls that sometimes allows other types of calls, but broadly none of the bugs have been serious security threats, and the few that have been discovered have generally been swiftly patched in the first two minor updates. Apple has yet to respond to this latest flaw and may still be investigating the issue.
While it's unknown exactly how widespread the issue might be, it doesn't affect all users. Anecdotal evidence suggests that users who upgraded early and have kept up-to-date with iOS 7 appear to be less prone to the issue than new 7.0.2 downloaders, but this remains unverified.