I have reset the SCM and also turned off all battery-saving functions (turning off hard-drives when possible etc.) - resetting PRAM isn't something that is going to help the situation, according to the relevant apple supprt page.
Doing these things unfortunately hasn't change anything 😟
I have early 2011 MBP, upgraded to Mavericks from directly Lion (Mountain Lion was too buggy for me).
It doesn't seem to make a difference if my laptop is connected to a power supply or not - as soon as it is left alone after going into sleep mode (including closing the lid or just leaving open for long enough for the monitor to go off), then I can only get to see the login screen, but after ~2 seconds, whether I click on the password-field or not, I get the beachball, which seems to be a neverending beacgball of doom - have left it for 20 minutes and it never got itself out of this limbo.
I have read a lot of forums, but nobody seems to have found a permanent solution to this whole debacle.
I will try an Apple Genius Bar sometime soon, but I won't hold my breathe there! Hopefully Apple will just release an update for Mavericks very soon!!