TV doesn't automatically show signal from Windows Media Center

This problem seems to affect many people (as per search engines) with the most suspected/mentioned cause being insufficient drivers from ATI (NVIDIA apparently has updated its drivers for related issues successfully, while ATI tried that too, but some users still seem to have the same issue afterwards).

Consequently you might try to find updated drivers for your video card, but you should probably try the following workaround first to confirm the direction: several users are having success with a little program called hdmiOn. You could try this too by assigning a Windows shortcut key to run hdmiOn.exe whenever you lose the signal.

For more details and/or different solutions you may find e.g. this thread helpful (rather lengthy though), which is addressing a similar issue and resolution experiments.

Update:

With hdmiOn fortunately providing a workaround now, theDude19 seems to be spot on regarding the actual cause being loss of Extended display identification data (EDID), as hdmiOn.exe is exactly enforcing a resend of EDID by simply turning the monitor off and on again.

Given the simplicity of this fix one would indeed think this to be the responsibility of the video driver, however, as usual, the handshake between the involved hard- and software entities might be insufficient on all sides...

Looks like the EDID is the problem. When you turn your TV off, the EDID of your computer video source is lost (since it is in memory in the TV).

According to wikipedia:

Extended display identification data (EDID) is a data structure provided by a computer display to describe its capabilities to a graphics card. It is what enables a modern personal computer to know what kind of monitor is connected. EDID is defined by a standard published by the Video Electronics Standards Association (VESA). The EDID includes manufacturer name and serial number, product type, phosphor or filter type, timings supported by the display, display size, luminance data and (for digital displays only) pixel mapping data.

The EDID is often stored in the monitor in a memory device called a serial PROM (programmable read-only memory) or EEPROM (electrically erasable PROM) and is accessible via the I²C bus at address 0x501.

When you turn your TV off, this ID is lost and causes the 'agreement' between the PC and TV to be lost as well. There are devices that can store this ID, such as this (note: I have no experience with these devices).