The timestamp formats on Blogger are a bit wonky. Here are the options I can select from:
In that screenshot, you can see a couple options are repeated twice: "10:23 PM" and "10:23:45 PM." Why are those repeated twice? I don't know.
For a while I've been using the "10:23:45 PM" format, although whenever I publish a post the timestamp shows "00" where it ought to display the seconds. It's not a big deal; I don't need to have my posts timed to the precise second. It just strike me as odd that the feature isn't working. I randomly checked 20 other Blogspot blogs, and none of their timestamps were broken down to the exact second, either.