Intuition is underrated. So let's call it something else. How about solid business experience or good judge of character or keen sense of team interaction. No matter what you call it the ability to detect a subtle change in a customer, vendor or employee can be crucial to business success.
One of our new hosts told me the following story. He went to a car dealership with the intention of purchasing a new car. He was approached by a salesman and "I gave off all the signals of buying but he never asked for the sale so I walked out". This salesman is in for a rough 2008.
Read the newspaper on any given day and some small business owner has been taken for $100,000 and never saw it coming. Of course it happens to big companies too - Societe Generale comes to mind.
Lots of things happen to business owners that can't be predicted. Yet those are the exact situations that cause the most problems. Take a few minutes and write down the most outrageous events imaginable: The salesman who won't ask for a sale, the trusted bookkeeper with a gambling problem, the sudden death of your forty year old operations manager, employees setting up a competing business, a nasty divorce settlement that includes the complete transfer to your spouse of the business you started before you got married.
While you'll hopefully never intuit a sudden death you can give the unthinkable a lot of thought. Then, when something doesn't seem quite right, you'll feel it. Even better you'll already have a plan.