This one’s for self-hosted WordPress users only. (Apologies to the rest of my readers.)
Ever since I started using WordPress for this blog in February 2009, I have been unable to automatically upgrade my WordPress software. (Manual upgrades worked — but they were a pain.) Then I switched to a real theme by WooThemes. Volia! The upgrade worked ultra-fast and with great perfection!
So if you are facing that problem, just change your theme to a more professionally coded theme.