Here's a quick script to automatically monitor your Google PageSpeed Insights desktop and mobile scores for a web page:
Note that this currently just logs the overall score. There are a bunch of other values returned (like number and types of resources on the page) that you could choose to monitor as well. It would also be easy to extend this to monitor more URLs, or to send you an email if the score drops below a threshold.
Updated May 5, 2019 to use version 5 of the PageSpeed API.