After a few days, I had no more shutdowns (previously, they happened most of the time). So in my case it seems clear that the ACPI Probe II sense driver (AMDA00) on my ASUS board was the main culprit than lead to frequent shutdown after variable, short times during password entry.
Like I said, there is also an unrelated shutdown after 60sec if I don't enter the password, but that doesn't bother me since I don't take me that long to enter my password.
So for other people with ASUS mainboards and quick (<60sec) or variable time shutdowns, from my experience I'd suggest updating the ACPI Probe II sense driver, which can be downloaded from the section of the ASUS website relating to your mainboard/motherboard.