Depending on your age and occupation, a DUI can have a serious impact on your career. Here in Florida, we have over a thousand miles of coastline, and therefore, a lot of citizens who make their living at sea. The U.S. Coast Guard has jurisdiction of seafaring licenses in coastal waters, and so it is the USCG that makes the rules about the effect of a DUI on your captain's license.
First, we should note that there are all kinds of captain's licenses. Licenses range from a "six-pack," or OUPV (Operator of Uninspected Passenger Vessels) license, which is a standard charter captain's license, to an unlimited tonnage license for a supertanker captain. And likewise, there are all kinds of DUI offenses--with or without crashes, 1st, 2nd or 3rd offense charges, at all levels of intoxication. So the Coast Guard does not treat DUI as a "one-size-fits-all" matter.
Following the Exxon Valdez disaster in 1989, the Coast Guard became much more active in investigating alcohol-related issues in U.S. mariners. These issues were not restricted to incidents at sea, but extended to alcohol related The Coast Guard imposed "assessment periods" for particular offenses. (An "assessment period" is just a euphemism for a suspension of the captain's license.)
It is important to realize that the Coast Guard definition of a "conviction" is much broader than you might think. If you had your license suspended for an alcohol-related offense, you have a conviction. If you entered a diversion program that required you to plead guilty or no contest, you have a conviction. If your DUI was reduced to Reckless Driving (even if the adjudication was withheld), you have a conviction.
After a DUI conviction, you will be asked at your next license exam if your drivers license has ever been "suspended" or "revoked." A "suspension" is what the Department of Motor Vehicles does. A "revocation" is what a court does. Otherwise, they are the same. So if you lost your license for any reason due to a DUI, the answer to that question by the Coast Guard is "Yes." The suspension will not kill your license, but answering incorrectly could.
In general, a single DUI will not result in the revocation of a Captain's License. But the failure to disclose the conviction is much more serious, so be honest. They are going to find out anyway.