A buffer by definition resists small changes in the pH of a solution (it maintains the pH). A buffer must contain the chemical species for “neutralizing” added amounts of acid or base. Generally, a buffer is a solution of a weak acid and its conjugate base (e.g. acetic acid and sodium acetate) or a weak base and conjugate acid (e.g. ammonia and ammonium chloride). If there is a lot of acid or alkali added then the buffer will not be able to cope with such a change and will no longer able to maintain the pH.
Buffers are most effective in the range PH = pK’a ± 1. Outside the range the concentration of either the acid or the conjugate base is too small to effectively resist the effect of added hydrogen or hydroxide ions.