If your Contact Form 7 suddenly is not working especially if you do have the plugin Jetpack installed, it could be due to some conflict caused by the newly Jetpack version 1.3 after your plugins update.
Solving the issue is pretty simple. You can just deactivate the Contact Form module under the Jetpack admin control. Click on the Learn More button and you will see the Deactivate button displayed. Click on the Deactivate button to deactivate the Contact Form Module. That’s all.