While it is hard to provide a definitive answer, once a blog is past the Google sandbox and new content is indexing relatively quickly, I’d say that virtually any blog can survive for 1-2 months of zero activity.
If you have a more developed blog, with a few dozen posts, 20+ DA, and your site is organically attracting back-links, you could probably take off several months. And even then, your blog would continue to grow for most of that time.
If you have a site with high domain authority, very strong back-links, several hundred or even thousand posts, lots of high value original content, and are a known authority in your niche, it is entirely possible you could go 6-12 months without adding a single blog posts and would see no adverse effect on your search engine rankings.
This is one of the great things about blogging. The product of your hardwork is realized in the form of compounded growth. While not fully passive at any point, blogging can be mostly passive at this point.
All of these time-frames that I suggested are based on the assumption that you are in a somewhat competitive niche, but not a hyper competitive niche. It also assumes that much of your content is evergreen and informational.
However, if you are in a niche that requires constant content updates, even a month or two can adversely affect organic search traffic.
Also, if you want to ensure your blog is constantly growing, I would never take more than a month or two off from posting some amount of content. Even just 2-3 high quality pieces, carefully interlinked with previous posts, can help drive forward momentum.
If you stop posting new blog posts but continue to update existing content, it is entirely possible that your site would be fine indefinitely.
Part of this depends on what you are doing to improve content, but part of it also depends on the general competition within your niche.
In a high competition niche (like, blogging about blogging, as this site does), you can never really stop publishing new content, because the competition is too fierce.
Conversely, in my other niche portfolio of blogs, many of my sites have few direct competitors, so it would take a rival blog well over a year to even cover all the topics I have, let alone do it in an original way.
In fact, in these less competitive and smaller niches, I will often post large amounts of content and then deliberately stop posting, in order to give search engines time to index and rank new content, and take some time to assess the performance of this new content, while allowing it to age.
This is one of the perks of having more than one blog to work on (rotating focus on content), but the same principle applies to any blog.