One possible reason for the odd distribution of the well known pink warning
Could not connect to Blogger.com. Saving and publishing may fail.
Cannot View Webpage
may be that it involves several different problems, coming together.
It's possible that Pete Hopkins explains one of the problems as a side effect of the cookies generated by Blogger, some of which are used in post editor.
Cookies are normally small and unassuming, but there's a bit of unusual behavior in that Blogger automatically saves the first few k of your post in a set of cookies as you're typing. That way, if your browser crashes you can use the "recover post" link to get at least the first part of it back. However, the side effect of using cookies in this way is that even though they're only being used (abused?) for local/offline storage, your browser will send the cookies with every request to a blogger.com server.
This might explain why some Bloggers report temporary relief by clearing cache and cookies, and other Bloggers report relief by making shorter posts - Publishing, then editing repeatedly.
Pete continues in his discussion, to suggest a workaround, to block the problem created by the cookies. You'll have a little script, that you'll have to run each time you start a post editor session. You run the little script, having previously saved it as a bookmark (favorite), from your browser.
* Go to Pete's website.
* Make a bookmark from the code that he provides, per his instructions.
* Each time that your browser links to a screen where the Blogger connection testing is done (anywhere you see the pink error message), execute the bookmark, created from Pete's website, after the page has loaded.
* See the WikiPedia article about bookmarklets, for more information.
Various Bloggers have reported mitigation of the well known pink warning, when using Pete's bookmarklet. Give it a shot, and see if it provides you any improvement to your problem.
Solution : stop post backup
Could Not Connect To Blogger.Com