This could happen for a lot of reasons. Look for JavaScript errors in the console of your web browser, if there is an error with another script it may also break the contact form.
We recommend using the Firebug extension for debugging if you do not already. If you enable the Net tab you will be able to see the Ajax requests being sent and received by the form and this can help to debug any problems you have in the PHP code because it isn’t obvious when working with an Ajax application.
A good way to check for errors is to disable JavaScript in your browser and submit the form, any errors that are in your PHP code will be sent to the browser instead of silently back to the JavaScript so this might help you find some problems.