Proof of buffers inability to maintain exact same pH
A buffer is a solution that can resist pH change upon the addition of
  an acidic or basic components. It is able to neutralize small amounts
  of added acid or base, thus maintaining the pH of the solution
  relatively stable.


Buffers do not maintain exact same pH, but keep it relatively stable i.e. close to the original value.
log(ratio) &lt;&lt; pKa, therefore, pH changes will be minimal, unless substantial amount of acid has been added to the solution.

For instance, when the ratio between the conjugate base/acid is equal to 1, the pH = pKa. 

If the ratio between the two is 0.10, the pH drops by 1 unit from pKa since log (0.10) = -1. 

If a ratio increases to a value of 10, then the pH increases by 1 unit since log (10) = 1. 

As you can see, changing ratio by 10 times, affects pH value only by 1 unit.