Mountain Lion won't wake up after an extended sleep
This is a known issue that hasn't been fixed as of 10.8.1. When Mountain Lion hibernates (either directly or as part of standby mode), it couldn't wake up and thus need to be restarted.

The current workarounds are:


Disable hibernate mode.
Disable standby mode.


I've written an article how to get around this issue by preventing OS X from hibernating.

For Apple folks: please see rdar://1212084 - Thanks.