Why does buffer capacity of tartrate buffer generally decrease as the buffer pH increases?
Generally, the maximum buffer capacity is at $\ce{pK_a}$ . The tartaric acid is somewhat special for 2 reasons:


It is a diprotic acid with both $\ce{pK_a}$ very close, with the $\ce{pK_{a1}}$ rather low, being affected by the reason 2. : 

$$\ce{pK_{a1}}=2.89,\ce{pK_{a2}}= 4.40 (L+)$$
The solution buffer capacity (not limited to presence of specific buffer substances) generally increases toward $\ce{pH}=0$. It means, the buffer capacity is not given by concentration of  of conjugated acid and base, but also by concentration of $\ce{H+}$ itself.
That in large extent masks the $\ce{pK_a}$ maximum. It means, at a slope, a local peak must be big enough to be a peak.