There’s a reported fix that works for some, though not 100%:
AppleInsider reported on Monday that a simple procedure has successfully eliminated the bug for many users:
• Disable iMessage in Settings -> Messages
• Reset the iPhone’s Network Settings under Settings -> General -> Reset
• Reenable iMessage.
While the method worked, and continues to work, for most iPhone owners afflicted with the iMessage bug, some have reported that the message failures reappeared after a few hours, forcing them to repeat the steps above.
There’s conjecture that the upcoming 7.03 update will contain this fix. Let’s hope so.