America has been imbued since its founding with a persevering spirit. From Ben Franklin to Horatio Alger to Rocky Balboa, the culture bombards us—children especially—with messages about the value of determination and grit in the face of adversity. This ethos is perhaps best captured in the enduring 19th-century maxim, "If at first you don't succeed, try, try again."

It's hard to argue with such an affirmative sentiment. And no wonder this never-say-die attitude has made such an appealing plot line for dime novels and Hollywood. But is it really good psychology? Or might there be times when it's better to simply give up?

Psychologists have been exploring this question, and more specifically a possible link between tenacity and both physical and mental health. It would seem on the face of it that persistence would be tonic over the long haul; hanging tough should increase the odds that you'll succeed, and personal success is closely linked to well-being. But what if the goal is extremely unlikely? Like an infertile couple conceiving a child? Or an average high-school sprinter becoming an Olympic gold-medalist? Is there a point of diminishing returns beyond which one failure after another takes a health toll? When does an admirable trait like perseverance start to look more like beating your head against the wall?

To test this in the laboratory, psychologists Gregory Miller and Carsten Wrosch developed a psychological instrument that can reliably distinguish between people who are relentless by nature and those who are much more accepting of life's curveballs. For simplicity, let's call them the Bulldogs and the Quitters. In a series of experiments the psychologists have exhaustively studied these two personality types to see how healthy and well adjusted they are.

And the answer is plain: Quitters are healthier than Bulldogs by almost every measure. For example, in one study the psychologists looked at everything from indigestion and diarrhea to skin disorders, poor sleep and headaches. Quitters suffered less than Bulldogs across the full range of maladies. Further, the Bulldogs' stress hormones were much more likely to be out of whack, indicating that they are in a state of chronic stress. And in a new study, published in the September issue of Psychological Science, the psychologists followed teenagers for a full year. Over that time the Quitters had much lower levels of a protein called CRP, an indicator of bodily inflammation. Inflammation has recently been linked to several serious diseases, including diabetes and heart disease, suggesting that healthy but tenacious teens may already be on the road toward chronic illness later in life.

But knowing when to throw in the towel is only half the story. The psychologists also sorted both the Bulldogs and the Quitters by their willingness to re-engage and set new goals after they gave up on something important. While they did not find a direct link between re-engagement and physical health, they did find that people who readily jumped back into life had a greater sense of purpose and mastery and were less likely to ruminate about the past. Setting new goals appears to buffer the emotional consequences of failure, especially for those, like the Bulldogs, who have the hardest time admitting defeat.