For a while my self-hosted WordPress has been a royal pain in the ass. Trying to compose through the WordPress.com interface through Jetpack would show occasional errors that “Saving of draft failed” or an inability to communicate. Sometimes it was usable, sometimes there were so many errors I gave up and used the site. The site admin interface sometimes made me login every hour or every couple minutes.
I reinstalled Jetpack a couple times. I poked around on the WordPress support forums which I apparently could not search.
So I searched via Google and ran across this How to Fix WordPress Keeps Logging Out Problem article. It dawned on me that I had let my hosting provider setup SSL for the site. The WordPress Address and Site Address fields were using http. So I changed them to https. That seems to have solved the login issues.
I am writing this through the WordPress.com interface and got a failure on saving the draft. So there is something else to make it all better.