I too have a tri-color beech and I just noticed a few of the leaves are turning a deep purple, almost black. I guess it is reverting but I can't see my self cutting off the branches! I wonder if they all do this reverting thing because i have another tri color and it is still the spectacular tri colors
What you have is the common 'Purpurea Tricolor' ('Roseomarginata'), thus the purple-pink-white combo. (Extremely rare, perhaps even extinct 'Tricolor' has no purple coloring). I have seen tall specimens that were still true-to-type (although the white often diminishes rather soon after planting, much to the consternation and bafflement of many). So, no, I wouldn't say it is usual for all-purple branches to appear.