Possible for batch size of neural network to be too small?
A batch size of 32 is commonly used and referred to as "small," but
  why don't we use a smaller batch size of 1 to guarantee convergence?


The issue is that a small batch size both helps and hurts convergence. Updating the weights based on a small batch will be more noisy. The noise can be good, helping by jerking out of local optima. However, the same noise and jerkiness will prevent the descent from fully converging to an optima at all. 

It is a trade off between these factors, the best batch size will depend on the shape of the error manifold. Larger batch sizes are better on convex errors and smaller batch size are good on errors with lots of deeper local optima.