It may take 30 seconds after the computer resumes before WMC can access the tuners due to the time it takes WMC complete the association process. This is normal.
If the tuners are not available after 30 seconds then something may be blocking UPnP SSDP communication.
Test case:
1) Run WMC and go into Live TV mode.
2) With live TV still playing, put the PC into sleep mode.
3) Wait for the PC to go completely into sleep mode, then power up again.
When you log in you should see WMC running, showing the guide.
4) Click the channel in the guide.
You may get an error if this is done within 30 seconds of resuming - just ignore it and wait - video should start playing after a short while.
If video does not start playing after 30 seconds then something may be blocking UPnP SSDP communication.
Firewall software:
If running any third party firewall software try repeating the test with the firewall disabled.
Windows Firewall does not interfere and does not need to be disabled.
DLink routers:
Some DLink routers block multicast traffic within the LAN by default (even between wired Ethernet ports on the router).
Use a web browser and log into the router:
http://192.168.0.1/
Click on the ADVANCED heading at the top, then click ADVANCED NETWORK on the left hand menu.
Test with "Enable Multicast Streams" enabled.
Test with "Enable Multicast Streams" disabled.