58 years ago - Nathanial Christopher Adam is born.
39 years ago - 19-year-old Nathan joins the air force, on his way to becoming a decorated combat pilot.
34 years ago - 24-year-old Nathan is wrongly convicted of killing a superior officer. He chooses to participate in a weapon experiment to earn a presidential pardon.
32 years ago - 26-year-old Nathan is bombarded with experimental radiation, causing his body to dramatically alter. He appears to atomize, but is instead lost in the timestream.
7 years ago - 26-year-old Nathan re-appears, but was presumed dead so he does not receive his pardon. General Wade Elling decides to use him as a government-controlled super hero under the threat of court-marital. He defeats Bette Sans Sovei.
5 years ago - 28-year-old Nathan proves his innocence & returns to active duty. He accepts an invitation to the Justice League after their membership is decimated in the battle with Doomsday. He assists the Suicide Squad, working alongside Bette Sans Sovei.
3 years ago - 30-year-old Nathan befriends Bette Sans Sovei after she is released from the Suicide Squad. He absorbs too much radiation during the White Martian attack on the Justice League and is again cast into the timestream.
2 years ago - 30-year-old Nathan re-appears from the timestream, resuming his roles with the Justice League & the air force. He and Bette Sans Sovei are engaged.
1 year ago - 31-year-old Nathan Adam leaves the Justice League with Jefferson Pierce to begin a Justice League Task Force for the American government.
There are several good ideas in Captain Atom's story, but as best as I can tell there hasn't been a solid attempt to solidify them into a single concept. The backstory is there, and the idea that he is a air force pilot from the past whose powers force him to periodically bleed radiation by leaping forward in time. He's had tenures with almost every variation of the Justice League, and he has the intriguing element in his story that he befriended and later married one of his own villains. that's interesting stuff.
So why isn't he more popular? I have no idea. the costume might be part of it. It's a cool costume, but it's pretty much tailor-made to make him a solid supporting character. There have been several attempts to re-imagine him as something more mass market, first as a bridge character with the Wildstorm universe and then during the new 52 as something far closer to Dr Manhattan, a character that's actually based on him. There was even Breach, a deliberate attempt to reboot the character that was editorially written off in the middle of his own story.
While it's frustrating that they can't seem to just tell a good story with what is clearly a solid character, you have to at least commend the fact that they're trying, despite the fact that all their attempts involve completely re-imagining a character that's pretty much fine as he is.