When you go to Help/About in the program, which version does it show you have?
In the fine print under the big letters "Adobe Premiere Elements 13", it should say "Version 13.1 (201501131.daily.767917)."
Is that not the case?
What operating system are you running?
Under the Help menu, does it show you as signed it?
Mine says Version 13.0 (20140903.daily.717136), I'm running Windows 10, and yes it does show me as signed into my Adobe account.
You're definitely not updating.
Do you antivirus other than Windows Defender? (Norton is notorious for choking off the good with the bad.) Try turning it off as you update.
And of course make sure you're running the program as an administrator.
Still nada . I disabled Avast, and ran it as admin and it still does the same thing. It closes out, updates in a new window, and then when it's done it re-opens and says it needs to update again.
I don't know what to tell you. It should be fully automatic -- or as simple as selecting Check for Updates.
You've clearly got some firewall or something up that's blocking it. I just don't know what it is.