How are food dyes affected by heat and ingredients?
As @GdD has said, a lot of the liquid dyes sold in the baking aisles of supermarkets while adequate for icing etc, are not really designed for baking. If you are intending to bake with a colouring, the powdered food dyes used in Indian and Chinese cooking can produce very deep colours, but they are nearly always synthetic and have been linked to some food allergies. The post What makes food dyes heat-safe? explains more about heat tolerant dyes and lists some good alternatives.