Both Asus and third-party utilities such as PcProbII/AISuite/CPUZ shows that my CPU Vcore reading drops as the CPU load goes up.
This also happens after I set CPU Vcore to a set value instead of the preset [AUTO].  Why does the motherboard act like this?
Will this effect the overall stability of my system?

Answer
As Intel specification clearly states Vcc (CPU Vcore) should drop in propotonal to the increase of Icc (CPU current consumption), in order to prevent causing permanent damage to your CPU. When CPU is under stress (in other words, under higher load), the current consumption of the CPU will go up, and the CPU Vcore will then drop to conpensate this change. This is a perfectly normal behaviour, and will not effect the overall stability of your system.

For more information, please refer to Intel CPU datashee, under "DC Voltage and Current Specification".