There are a number of reasons that an automatic update could fail. Jetpack is a large plugin, with many modules and language files. This can cause issues with some servers when using the automatic update.
Could you please try manually reinstalling Jetpack? To do so, download the Jetpack plugin here:
http://downloads.wordpress.org/plugin/jetpack.latest-stable.zip
Then, log in to your site via FTP, and delete the existing Jetpack plugin folder. You should then be able to reinstall the plugin manually by following the instructions here:
http://codex.wordpress.org/Managing_Plugins#Manual_Plugin_Installation
I would strongly recommend that you make a complete backup of your website before trying this.
There are a few more steps involved, but it will allow you to update the plugin without the risk of a failed automatic update.
I hope this helps! Please let me know if you have any questions.
