What separates those who lead well in hard times from those who don't?
First, those who lead well in hard times do not tend to take the situations as personally as others. Not that it is easy or comfortable. It helps, however, to realize that we are often targets because people disagree with our decisions or don't fully understand situations we cannot be candid about. The price of leadership is that we will be misunderstood at times and that we will be a target because of decisions we must make.
Second, leadership in hard times is easier when we keep our anxiety low. Anxiety is wasted energy. If we will take the time to gain perspective from others and from God we can usually respond with greater wisdom than when we respond on the fly - or out of anxiety and anger. That is a skill that can be learned even when it is not native to our skill set.
Third, leading in the hard times is easier when we take a long view rather than a short view. In the moment there may be uncertainty and pain and conflict. In the long term good decisions yield health and effectiveness. Thinking long term allows us to weather the short term discomfort. In fact, those who think short term often respond poorly to hard issues because they are not willing to live with short term pain for long term gain.
Fourth, leading in hard times is easier when we trust in God's sovereignty. Sure, not all things are solved this side of heaven. At the same time, God has a way of working things out when we respond in a measured and wise way rather than allowing our emotions to hijack our actions in unhealthy ways.
Leading in the hard times is actually one of the fundamental ways that leaders grow and mature: If we respond with wisdom rather than with emotion.