In late 2010, Blogger Support announced that they cannot provide the service to restore deleted posts.
Once you (the blog owner) delete a page or post, it's gone - though we have asked for a recovery option. Fortunately, there are several possibilities, to recover deleted pages or posts - though some work may be required.
There are several possible techniques, for recovering one or more deleted pages or posts,that were previously published.
The choices of recovery / restore may depend upon how the deletion / removal occurred.
Deleted by Blogger - saved as Draft, because of DMCA violation accusation.
Deleted by you - visible in search engine cache.
Deleted by you - visible in blog feed.
The post was saved as Draft, because of DMCA violation accusation.
If Blogger deletes a post, because of an accused DMCA violation (righteous, or spurious), you'll find the post saved as Draft. You can, possibly, republish the deleted post(s) - though if you don't have the DMCA Violation accusation resolved, you risk having your Blogger account and blog deleted as a repeat and unrepentant offender.
The post may be retrievable from search engine cache.
If you can find the content of the post, in search engine cache, you can retrieve the PostID. Knowing both the BlogID and the PostID, you can edit the post, and re publish it.
If I was to delete this post, I (or another blog administrator), when logged in to Blogger, could edit this post, and Publish it again, using the Post Editor URL and the PostID - possibly with some extra effort.
You should see some or all of the following detail, in the top portion of the post, that you find in cache. You can find "blogID" in other areas of the template. "postID" may be a bit elusive, though.
Recovering A Deleted Page Or Post
Using "blogID" and "pageID" / "postID", I can build the recovery URL:
https://www.blogger.com/blogger.g?blogID=24069595#editor/target=post;postID=8899607620317019913
Similarly, for a deleted page,
https://www.blogger.com/blogger.g?blogID=24069595#editor/target=page;pageID=8872543322493900789
Alternately,
http://www.blogger.com/post-edit.g?blogID=24069595&postID=8899607620317019913
or
http://www.blogger.com/page-edit.g?blogID=24069595&pageID=8872543322493900789
Using the above technique, and substituting your blog and page / post, you can recover the entire page or post, including all content and formatting - and the original URL. This technique won't work for un indexed blogs, or for new pages, however. Private blogs are unlikely to be indexed, also.
In some cases, even if you're able to retrieve the postID and recover the post editor session, you may be unable to re publish. If you get a bX error when re publishing, copy the contents from HTML mode - then make a new post, and paste. After you publish the new post, under a new URL, you'll have to add a Custom Redirect, from the Old URL to the New URL.
The post may be retrievable from blog feed.
You may, with a little work, be able to retrieve the BlogID and PostID from the blog posts newsfeed, using a text browser. In that case, you can re publish the post, using the above URL construction. I'm not sure that this technique will work, for pages.
If search engine cache isn't available, and if the blog publishes a post feed, you can possibly subscribe to the post feed in Google Reader or a similar feed reader, and retrieve the text content of the post. Having the text of the missing post visible to you, you can copy and paste the content, into post editor, and Publish the post again.
Feed content retrieval will provide text, which must be reformatted.
Using this technique, you'll have to reformat the post content, as feed content is formatted relatively simply. When you publish the post, it will publish as a new post, with a new URL. Again, add a Custom Redirect, from the Old URL to the New URL, if you want to retain post reputation. This technique won't work for private blogs, or for blogs where the feed is disabled.
So, if you delete a post, or if Blogger deletes it on your behalf, there are various options for recovery - though neither search engine cache nor blog feed options will likely work, for private blogs. And some options may be more or less desirable than others.