When “The Sopranos” ended with its infamous black screen in June of last year, many of the show’s dedicated fans were furious. People had fallen in love with emotionally complicated crime boss Tony Soprano and had tuned in episode after episode, only to have the show come to an unceremonious end less than an hour after Tony’s intricate web of conflict had finally unraveled. I sympathize with those who felt cheated, but I’ve grown to realize that “Sopranos” fans were the lucky ones.

It may sound strange to praise a long-running show—six seasons over eight years—for knowing when to quit, but the fact is that David Chase and the rest of the “Sopranos” team realized the limits of their storyline. Shows driven by complex antihero protagonists thrive on anticipation, with loyal viewers tuning in each week to see when the main character’s internal conflict will finally reach its boiling point and lead to either his downfall or triumph. The problem is that once the peak of the character’s storyline is reached, much of their intrigue is lost.

“The Sopranos” addressed this issue by making the culmination of Tony’s character the end of the series instead of forcing fans to watch the show deteriorate. Now, two of my once-favorite shows are failing to deal with the antihero concept as gracefully, prompting me to wonder if producers need to realize that the most interesting characters should have the shortest lifespans.

Consider Fox’s medical drama “House,” now in its fifth season, which stars Hugh Laurie as brilliant case-cracking doctor and miserable Vicodin addict Gregory House. For the first two and a half seasons, the show had great writing that focused on House’s painful personal history, his dry wit, and the tension between his hatred of people and his drive to save their lives. Viewers like me were treated to continual glimpses of his good and bad sides, wondering which one was the real House and which would win out in the end.

Unfortunately, we found out more than a year ago. By the second half of season three House ended up alienating his staff and causing them all to leave his department, but not before he convinced them all he had cancer in an attempt to get high at an experimental drug trial. In the last season and the start of the current one, he’s worked to ruin the marriage of one of his new staff members and accidentally caused the death of his best friend’s girlfriend, for which he shows no remorse. This is, of course, all in a day’s work for House, but he’s lost his moral tension, and the show is left to rely on awkward side stories involving a goofy private eye and increasingly uninteresting patients.

Another show in a similar state of stagnation is “Dexter,” Showtime’s series about a serial killer who lives a double life as a forensic scientist and devoted boyfriend. The catch is, he’s been brought up to kill only those who deserve it. The problem here is that the show built up too fast, and by the end of the second season Dexter had already evaded a statewide manhunt for the “Bay Harbor Butcher” and the only person who knew the truth about him was dead. Now the show lacks the suspense that made it so gripping, instead relying on a series of subplots. These include Dexter befriending a prosecutor whose brother he accidentally murdered. The prosecutor is played by Jimmy Smits, who after “The West Wing” is surely accustomed to being cast in dying shows. After escaping the police last season, Dexter seems more confident than ever in his murderous pursuits, and the show lacks most of the doubt and paranoia that made his character fascinating in the first place.

So what is to be done about these failing antihero dramas? First of all, if a series wants to maintain quality over several seasons, writers need to show some patience. Having a vigilante murderer come within spitting distance of the death penalty is a plot device that requires a longer buildup than just two seasons. Second, when the plot is failing, return to the writing. Witty and interesting dialogue was always a higlight of these shows, and it might be able to sustain them; maybe if the writers were more careful, they could make the protagonists seem less one-sided toward their demons.

It’s painful to watch the shows I once loved die out. Now that the titular antiheroes of “Dexter” and “House” have shown their true colors and moved past their main conflicts, everything seems like a mind-numbing extended coda. But being the procrastinating student I am, I’ll probably make up excuses to keep watching, hoping that the producers either find a way to re-complicate their characters or finally let them give way to a black screen.

—Columnist Jeff W. Feldman can be reached at jfeldman@fas.harvard.edu.