First, search engines do not rank websites, they rank individual web pages. Rankings are based on the relevancy of the content contained on the page, as well as the content on the pages that link to your page.
Naturally, if you update your blog with new content, you have changed the basis for your rankings. You should expect your rankings to change. The typical blog configuration will replace the top post anytime you add a new post. Eventually, content that was contained on the Posts page will be pushed off of that page as new content gets added.
This does have a significant effect on rankings for your Posts page, and the typical blog is configured to use the Posts page as the homepage. Therefore you should expect a great deal of fluctuation in your homepage rankings if you are updating your blog on a regular basis.
Likewise, when you create new backlinks you are also influencing the relevancy signals that search engines use to rank your pages and that too can cause your rankings to go up or down based on those altered signals.