It looks like the problem was that my ASUS U46E (BIOS Version 2.01.1204 American Megatrends) did not go to sleep properly. Or at least, could not wake up anymore.
So I changed the Power Options:
1) Never go to sleep.
2) Pushing the power button (and closing the lid) makes it go to hibernate.
I have an SSD drive so hibernate (even with 8GB RAM) does not take much time.