Probably other ways, but this one will work, that is how family assets are handled many times and also can handle tax complications cleanly etc. There are multiple legal structures btw that accomplish the same thing. If it is truly critical this is the tried and true way to make it happen at least to my knowledge.
If it up to 1 year, find a company that lets you pay up front and pay up front. Also cover domain registration as well.
It becomes harder the longer you go though, with time frames like 50 years you'll be looking up trusts and etc.
As other commenters have said, it's definitely tied to the length of the time you want your blog to be available. For 10 years, I'd run a quick script to crawl the blog (http://www.mooreds.com/wordpress/archives/3172 documents how) and push it up to s3 or netlify. For either, I'd set up a prepaid credit card to pay for the expected traffic times 3. You can also prepay for your DNS names.
You might need to write up some instructions for a friend to do the final sync and switch over DNS.
Your question is a very interesting one, because it blends themes of persistence, visibility, and accessibility within the context of the web...
Before we talk about the web, let's talk about persistence outside of the web... to gain persistence of your writings outside of the web, you could collect all of them into a book, and physically publish that book.
That would make your writings somewhat persistent, although, perhaps not as accessible as they would be if they were on a website.
But alas, the web changes over time.
Web site hosting companies come and go, and freely hosted web page providers frequently change hands and become subject to owners with new terms, conditions, and inactivity deletion policies... If I recall correctly, Geocities or Tripod (both free hosting providers), one or the other went out of business and lost thousands of free pages that people had created... so it's not guaranteed that any given free hosting provider will be in business 5, 10, 20 years from now...
A few ideas...
1) Put the same blog on multiple free blog hosting providers. That way if one goes down, it will still be mirrored by the other providers.
2) Make sure all of those blogs are indexed by the Wayback Machine: https://archive.org/web/ (The Internet Wayback Machine will probably stick around for awhile...)
3) I suppose you could write a book, and then if the book became a literary classic, like say, The Bible, then it would it would be copied and printed and re-printed throughout history. (On the other hand if your book didn't become a classic, then it wouldn't be reprinted, copies of it would be progressively harder to find, and at least in physical printed form, as more time went by, it might not achieve persistence...) But if you did write a book, you could probably get it on Google Books and on Amazon's electronic shelves (you'd probably want to make it free), and there it might stick around as long as Amazon and Google are in business... which might be reasonably decent persistence...
4) Oh yes, you'd probably want a legal notice in your writings saying that anyone can copy them at any time and for any reason -- or whatever set of conditions you'd prefer to apply. But keep in mind, the less conditions you apply, the more other people will be willing to freely copy and share the material, resulting in more persistence...
5) You could additionally put your writings in audio/video formats and upload them to YouTube and other video/audio hosting services.
6) You could host your writings (in whatever media format(s)) on P2P networks... if enough people downloaded them, they might stick around for awhile...