Have you tried sending iMessages on more than one Wi-Fi network?
Try the suggestions in this Apple doc -> iOS: Troubleshooting Messages
- To send and receive iMessages, your device must have a valid cellular or Wi-Fi data connection.
- Ensure that iMessage is turned on in Settings > Messages.
- iMessage registration validates your Apple ID for use with iMessage. If you are unable to activate iMessage, follow this article.
- If iMessage is unavailable either on the sending or receiving device, SMS will be used. You can turn this on or off in Settings > Messages > Send As SMS. Carrier messaging rates may apply.
- Verify that the Apple ID or phone number is listed in Settings > Messages > Send & Receive.
Note: To receive iMessages sent to your phone number on your iPad, iPod touch, or Mac, you must meet the following requirements:
- iPad or iPod touch using iOS 6 or a Mac using OS X 10.8.2.
- Verify that you are signed in to your Apple ID account on Settings > Messages > Send & Receive.