During a crisis, we can only deal with the urgent - and that rarely includes building relationships. If you are only communicating with others when there is an urgent problem, you are setting up poor relationship patterns and damaging your effectiveness.
At best, issue focused communication will produce simple accomodatation of your immediate needs.
At worst, your calls and emails will be met with "What, another problem?"
So don't wait for a crisis. Spend a few minutes each day with someone, simply talking about - listening to! - the bigger picture. The agenda is understanding, not immediate problem solving with your colleagues. Think out loud with them. Sow seeds for the future. Learn a little more about them as a person - and let them learn about you. Step away from your monitor for a few minutes and connect face to face with your peers, your staff, your boss. If you are part of a distributed group, do it with a phone/video call.
Then, when a crisis hits, you'll have more information and solutions for the long term, and more social capital in the system for executing those solutions.
We do this externally with our customers; we should apply the same best practices internally as well.