SUCCESS!!! I was able to workaround it! This is the unofficial workaraound for ATI 650 standby problem:
1. Download DevCon http://support.microsoft.com/kb/311272/
and extract it to C:\\devcon
2. Download HibernateTrigger http://www.rpi.edu/~desimn/suspendtrigger/
and install it.
3. If ATI 650 are the only ATI cards in your system, skip to step 5.
4. If you have other ATI cards in your system, you may want to restart only the 650 tuners. For this, open command line window and run: devcon find PCI\\* - this will produce a list of all local devices. Find ATI Unified AVStream Driver, and note the device IDs for your 2 tuners. In step 5, replace PCI\\VEN_1002* with a similar string that will identify only the ATI 650 tuners.
5. Create C:\\devcon\\ati650.bat file with the following contents:
net stop "Media Center Receiver Service"
devcon restart PCI\\VEN_1002*
net start "Media Center Receiver Service"
6. Open HibernateTriger, and type C:\\devcon\\ati650.bat in what you want to execute on resume.
Enjoy dual ATI 650 with stand by support!!!
Credit goes to denyart and hveijk!