Often times, if they had served conspicuously it had no negative impact on their careers.

2 we can look at here. One is Elliot Buckmaster, who was Captain of the YORKTOWN, he had assumed command in Feb of 1941, and led her through the first 6 months of the war, the early carrier raids, Coral Sea, and her sinking at Midway. He even led a party aboard the abandoned ship and had gotten her under tow when an IJN sub found her and finished her off with torpedoes.

He was then placed in command of the Navy's Primary Flight Training program, using his experience as one of the 2 most veteran carrier drivers in the navy to publish the fleet's first wartime flight training manual, and the massive expansion of the home of naval aviation in Pensacola. Her also put on his first star and became a Rear Admiral at this time, and was then sent back out in 1944 as the Commander, Western Carolines Operating Area. He retired a Vice Admiral.

We also then have Charles McVay, the CO of the INDIANPOLIS, who of the +300 ships to be lost by the USN in the war was the only one Court martialed over it. Found guilty for not "Zig Zagging" despite testimony from the Capt of the Japanese Sub that sunk him, he was exonerated by Nimitz, and even promoted eventually to Rear Admiral, but he never again held a command and was mostly in staff duties for the few years he remained active.

Most experiences fell somewhere in between, but those are just 2 notable cases of Captains who lost prominent ships to enemy action.