Personally, what I'd try to do is delete the JetPack folder via FTP (wp-content/plugins/jetpack) and redownload, reactivate to verify that there wasn't an issue with the initial update.
Another idea if that it may be a conflict between JetPack and another plugin on the site. One way to check is to deactivate all of your plugins, activate only Jetpack and see if the undesired behavior continues. If it doesn't, then there's a conflict. I'd re-activate plugins one-by-one until the situation occurs again. That way, at least, the Jetpack folks and the other plugin's developer would have an idea of where the problem may be.
I see that you posted over in the Jetpack fourms too. Hopefully, their folks will have other suggestions too!