It hasn't been once a month for several years - the move to "Big Daddy" and dynamic ranking updates (in 2006) changed all that. And then the move to the "Caffeine" infrastructure (2009-10) gave them the ability to dynamically update much smaller parts of the index insteaad o doing big chunks at one time.
Clearly today Google classifies sites and pages and various ways, crawling and indexing some much more frequently than others. As you said, sometimes new content is indexed in just a few minutes after publishing.
Google's index changes everyday. That does not mean Google is changing how your website is indexed is everyday. Some web pages are deemed very important and so Google will update them everyday. Other pages are deemed to not be important and so Google may only update them once a month.
If you want your pages to be crawled by Google more often you need to generate signals that Google will notice and realize that your page is important. Start with the minimum requirement of having significant amount of unique and valuable content on the page. Then develop high quality & quantity of backlinks.
Google updates all the time. They are constantly keeping an eye on your site with over 200 ranking signals. Link quality and quantity, content, bounce rate, amount of time spent on site, click through rate, etc.