Mine does the same, did you find a solution yet?
Try reinstalling the current version of WordPress… manually if you have to. If it won’t let you after that, follow the manual upgrade instructions as given here: http://codex.wordpress.org/Upgrading_WordPress
After getting it to 2.8.3, see if the automatic upgrade works again for 2.8.4.
Just in case you didn’t already disable all plugins before attempting the upgrade, do that first, before trying any of the above. The easy way to disable plugins is to rename the wp-content/plugins directory until the upgrade completes. You want this renamed no matter what method you are using for upgrading.
I like to change my theme to the default theme before upgrading, too, just in case the theme tries to break something.
Solution:
before you update – deactivate all plugins – don’t forget to reactivate them after the update.
uh… crazy… but mine worked the 4th time I tried it… I think my godaddy server was just sooooooooooooooooooooooooooo slow that it took a few tries. I did not have to disable any of my 10 plugins.
Did I mention that godaddy servers are soooooooooooooooooooooooooooo slow. They say 45 second website loading for WP sites is acceptable because it is a shared server…. I asked how long they are willing to wait for their phone to connect when they dial a number…. no response….