We have no reason to expect the quality of intuition to improve with the importance of the problem. Perhaps the contrary: high-stake problems are likely to involve powerful emotions and strong impulses to action.
An executive might have a very strong intuition that a given product has promise, without considering the probability that a rival is already ahead in developing the same product.
When you are under time pressure for a decision, you need to follow intuition.
You should not take your intuitions at face value.
There are some conditions where you have to trust your intuition.
Many ideas happen to us. We have intuition, we have feeling, we have emotion, all of that happens, we don't decide to do it. We don't control it.
I would be wary of experts' intuition, except when they deal with something that they have dealt with a lot in the past.