One of the significant challenges is figuring out how to use 42ms (the frame duration on fastest speed) of computing time to decide what actions, if any, to take next. You don't have the luxury of taking many minutes to decide one move as you would in a game like chess or go. You also don't alternate taking discrete turns with your opponent, despite having discrete frames. It may be best to not take an action in a given frame. This is particularly true if the AI is attempting to stay under an APM threshold, as it has to decide if an action is worth the opportunity cost.
It is also necessary for a quality SC AI to remember what has happened in the past. A chess board position is identical regardless of how the game got there, but this is not the case in StarCraft. An AI has accumulated lots of information about its opponent that is no longer visible to it in the current frame (unit movements, gas/mineral counts, number of workers active, etc), and this needs to be recalled and play into decision making.