I also have the same problem. Have been at it for 2 days and haven't come close to a solution.
What I learnt is that the system should shut down to a G2 (s5) state (see http://en.wikipedia.org/wiki/Advanced_Configuration_and_Power_Interface to learn about ACPI) however seems to do so for a short amount of time, maybe for about half hour or so. Then totally shuts down.
I have a onboard Realtek RTL8101E 10/100.
I get the following results:
$ acpitool -w
Device S-state Status Sysfs node
1. P0P2 S4 disabled
2. P0P1 S4 disabled pci:0000:00:1e.0
3. PS2K S4 disabled pnp:00:0d
4. UAR1 S4 disabled pnp:00:0e
5. EUSB S4 disabled pci:0000:00:1d.7
6. MC97 S4 disabled
7. HDAC S4 disabled pci:0000:00:1b.0
8. P0P4 S4 disabled pci:0000:00:1c.0
9. P0P5 S4 disabled pci:0000:00:1c.1
10. P0P6 S4 disabled
11. P0P7 S4 disabled
12. P0P8 S4 disabled
13. P0P9 S4 disabled
14. USB0 S4 disabled pci:0000:00:1d.0
15. USB1 S4 disabled pci:0000:00:1d.1
16. USB2 S4 disabled pci:0000:00:1d.2
17. USB3 S4 disabled pci:0000:00:1d.3
Now I figure it is either hardware related or there is someway to configure the shutdown process to do what we want.
$ ethtool eth0
Settings for eth0:
Supported ports: [ TP ]
Supported link modes: 10baseT/Half 10baseT/Full
Supports auto-negotiation: Yes
Advertised link modes: 10baseT/Half 10baseT/Full
Advertised auto-negotiation: Yes
Port: Twisted Pair
Supports Wake-on: pumbg
Current message level: 0x00000033 (51)
Link detected: yes
I haven't found any info yet on how that possibly could be done. Maybe it requires patching the kernel but that is beyond my "relatively recent move to Linux" capabilities. I'm still looking.