Buffer solutions have constant acidity and alkalinity because

If small amount of an acid or alkali is added to a buffer solution, it converts them into unionised acid or base. Thus, its $\mathrm{pH}remains unaffected or$in other words its acidity/alkalinity remains constant. e.g., $$\begin{aligned} \mathrm{H}_{3} \mathrm{O}^{+}+A^{-} \rightleftharpoons \mathrm{H}_{2} \mathrm{O}+\mathrm{H} A \\ & { }^{-} \mathrm{OH}+\mathrm{H} A \longrightarrow \mathrm{H}_{2} \mathrm{O}+A^{-} \end{aligned}$$ If acid is added, it reacts$with A^{-} to$form undissociated HA. Similarly, if base/alkali is added, \mathrm{OH}^{-}combines with \mathrm{H}$A to$give \mathrm{H}_2 \mathrm{O} and $A^{-}$ and thus, maintains the acidity/ alkalinity of buffer solution.