Trauma is bad. You want to avoid that.
Know it is unlikely for your child to be traumatized as long as you are sensitive and mild, not pushy, and do what is suggested in May’s answer—which I recommend as a practical guide, unlike my more theoretical treatment. However, it seems to me valuable for you to understand why approaching such a situation carefully is worthwhile. While it would likely have to be some pretty scary and either severe or oft-repeated negative events to be truly scarring, just know that things can be traumatic in surprising ways. The perception of the child rules all other considerations, and PTSD developed as a child seems to be more damaging than that incurred as an adult.
Children should only be challenged to the point of medium discomfort, that only occasionally, and always with the proper emotional and cognitive support. It is crucial that your child feels he or she has choices—even if ultimately those choices only give the illusion of control. If an event already happened that did exceed a child's ability to deal with, a trusted adult talking it over with the child (without making a big deal of it) is helpful—the goal is to give the child a helpful narrative to assign to the event that explains it at the child's comprehension level and provides the child with awareness of choices1 in the future to deal with that sort of situation. This talking also needs to be in balance as the talking itself can become a charged, implicit narrative that makes the situation more frightening—so in some ways it's important to show more than tell, if possible, while helping the child unknowingly construct/accept a helpful narrative.
Overall, children need to be protected from situations and input beyond their age and maturity level that cause them to start creating maladaptive coping mechanism of any kind—emotional, intellectual, or otherwise. And, consider the very important factor that the definition of maladaptive here is adaptive to the current situation beyond the child's ability to handle, but maladaptive to his or her future adult function as a whole person. Specifically, if the cortex shuts down and the limbic system or "reptile brain" are left in charge2, having that occur with great severity or repeatedly in mild severity3 is a recipe for long-term emotional damage and other problems3 later in life.
In closing, keep in mind that executive function takes until around age 25 4, 5 to finish developing, and it may take up to age 31 for highly gifted people. While executive function development can be accelerated with the right kinds of teaching, you're never going to vastly exceed the physical brain development stage of the child, so it's important to be aware of a child's hard limitations and work wisely within them instead of unwisely ignoring them...
My comment: While this article is about bullying, the effect on children of dealing with traumatizing circumstances is the same regardless of whether the source of the trauma is a bully or not.
Coping strategies: mediators of long-term effects in victims of bullying? Annuary of Clinical and Health Psychology, 2 (2006) 15-25
On one hand, when we considered the perception of control, the victims with less perception of control on bullying episodes showed higher stress levels. On the other hand, students who considered the conflict more as a challenge than a threat experienced lower levels of stress in adult life. ... [E]ven if the perception of control was imaginary, the stress buffering finally reinforces it. ... The perception of control may be considered an efficient protector in victim populations.
How Terror Hijacks the Brain
"if the cortex shuts down and the limbic system or 'reptile brain' are left in charge":
Maia Szalavitz, TIME Magazine, April 16, 2013 When the brain is under severe threat, it immediately changes the way it processes information, and starts to prioritize rapid responses. “The normal long pathways through the orbitofrontal cortex, where people evaluate situations in a logical and conscious fashion and [consider] the risks and benefits of different behaviors— that gets short circuited,” says Dr. Eric Hollander, professor of psychiatry at Montefiore/Albert Einstein School of Medicine in New York. Instead, he says, “You have sensory input right through the sensory [regions] and into the amygdala or limbic system.”
Posttraumatic stress disorder and the nature of trauma
"repeatedly in mild severity":
Initially described as resulting from a onetime severe traumatic incident, PTSD has now been shown to be triggered by chronic multiple traumas as well.
"long-term emotional damage and other problems":
Traumatic events such as family and social violence, rapes and assaults, disasters, wars, accidents and predatory violence confront people with such horror and threat that it may temporarily or permanently alter their capacity to cope, their biological threat perception, and their concepts of themselves. Traumatized individuals frequently develop posttraumatic stress disorder (PTSD), a disorder in which the memory of the traumatic event comes to dominate the victims' consciousness, depleting their lives of meaning and pleasure.
Maturation of the adolescent brain , Neuropsychiatr Dis Treat. 2013; 9: 449–461. Published online 2013 Apr 3. doi: 10.2147/NDT.S39776
"executive function takes until around age 25 to finish developing":
It is well established that the brain undergoes a “rewiring” process that is not complete until approximately 25 years of age. This discovery has enhanced our basic understanding regarding adolescent brain maturation and it has provided support for behaviors experienced in late adolescence and early adulthood. Several investigators consider the age span 10–24 years as adolescence, which can be further divided into substages specific to physical, cognitive, and social–emotional development.
Sylwester R. The Adolescent Brain: Reaching for Autonomy. Newbury Park (CA): Corwin Press; 2007)