Not necessary. At the current price level, the miners can continue mining with a comfortable profit margin. That is without considering the prospect of bitcoin becoming a widely used mechanism for financial transactions. Since, the difficulty did not substantially decrease even when the prices was hovering around $2.00, it is very unlikely we will see any substantial decrease after the reward is halved. Whether it will go substantially up or not, that is still uncertain. My feeling is, with the availability of ASICs, difficulty will go up in the future.
You think that halving the reward will not impact the amount of people mining?
Of course, halving the reward will half the amount people mine. Irrespective of the difficulty, the rate of mining is constant. I am only saying that there may not be a substantial drop in difficulty after the reward is halved if the price remains at current level. If the price goes up, the difficulty will go up as the profit margin will be larger.