If you want your blog to be secure:
1. Own your domain name, you can always move your blog and keep your traffic if you own the domain name.
2. Use a service that allows you to backup your blog to your home computer.
3. keep your blog software up-to-date
The reason that sites like blogger shut down bloggers is typically due to a terms of service violation or a particular view on a topic.
Here are some quotes from people who have run into this situation:
My website, which has to do with mortgages, was shut down by Blogger because they thought that it was a spam website. Everything is related to mortgages, so I don't know how and why they are considering it to be spam
I only just realised that Blogger are closing down ftp webhosting blog support on the 1st of May. That means, this blog will no longer function!
This is a big one, there was a big political uproar over a blog and google shut it down:
A few weeks ago I started receiving ‘Google & Blogger warnings’ from my technologically savvy friends and well-wishers, who encouraged me to have a mirror site as a back up and or cease using Google’s Blogger all together. I did take these warnings seriously and started looking at alternatives and other options.
Google told Edmonds her blog is considered “a potential spam blog” and it would be deleted in 20 days. Google admitted its “automatic spam detection” is “fuzzy” and occasionally blogs not involved in spam are “flagged incorrectly.” 123 Real Change, however, was not “flagged incorrectly,” the same as Alex Jones’ videos posted on YouTube were not erroneously singled out to be deleted. Google works directly with the government to remove content.
The problem with using free services is that you have no rights and in many cases no recourse. With a blog service like blogger you can't even make a traditional backup of you blog to restore at another location.