Does dilution of a buffer affect pH?
In the Henderson-Hasselbalch equation, $K_\mathrm{a}$ is a product of concentrations and considered a constant.

In reality, $K_\mathrm{a}$, when defined as a product of concentrations, is not a constant:



Upon dilution (decrease in ionic strength) the $\mathrm{p}K_\mathrm{a}$ will change, and therefore the pH of the solution will change. 

In addition to the above reason, pH will always approach 7 at extreme dilution as it approaches being pure water.