The pH of the buffer solution does not change appreciably because the strong acid (free H⁺) reacts with conjugate base of buffer producing more weak acid. pH formula of buffers is (Henderson-Hasselbalch formula):
pH = pKa + log ( [A⁻] / [HA] )
The addition of strong acid decreases [A⁻] increasing [HA]. pH change just in the log of the ratio of [A⁻] with [HA], that is a real little effect over pH of the buffer solution.
