If a child is forced to deal with situations that are beyond his or her ability to understand, process, respond to, or control—specifically, situations that are accompanied by strong negative feelings, this may be traumatic.
Trauma is bad. You want to avoid that. Exposure to a traumatic or aversive event is now recognized as a vital cause of an entire class of conditions affecting mental well-being1.
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 traumatic2 in surprising ways.
In my opinion 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 choices3 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 charge4, having that occur with great severity or repeatedly in mild severity5 is a recipe for long-term emotional damage and other problems5 later in life.
As a child over time develops physically, mentally, and emotionally, and becomes more sophisticated, mature, and capable of understanding and exercising good judgment, he or she can tolerate more and more stimulation and more and more exciting/scary/intense situations. So long as the level of these things is within (or just barely outside) the child's competent operating envelope, then he or she will continue to remain confident, capable, adaptive, and functional.
Good modeling of behaviors and attitudes by parents, plus assisting a child to identify, label, feel, and respond to his or her emotions, are both always of critical importance to children for their proper development, whether or not any trauma has occurred. You can research Childhood Emotional Neglect to understand one aspect of this a little more, and to gain an idea of what kinds of intentional interaction with a child will help him or her to develop emotional intelligence in a healthy way and at a normal developmental stage. That emotional intelligence will then allow the child to use his or her own emotions and the emotions of others for positive outcomes instead of negative ones.
In closing, keep in mind that executive function takes until around age 25 6, 7 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...
Laura K. Jones, Jenny L. Cureton, Trauma Redefined in the DSM-5: Rationale and Implications for Counseling Practice The Professional Counselor Journal, Volume 4, Issue 3, Pages 257–271 doi:10.15241/lkj.4.3.257 (more details and formats)
Note: This is a great overall explanation of what (adult) PTSD is and how it arises. Through focusing on the differences between previous DSM definitions of trauma, a pretty thorough treatment is accomplished. Note that the adult criteria are distinct from criteria for children.
DSM-V PTSD criteria for children, summarized by verywellmind.co].
Claim: "... know that things can be traumatic2 in surprising ways."
The perception of the child rules all other considerations for how traumatic an event is, and PTSD developed as a child seems to be more damaging than that incurred as an adult. While the criteria for PTSD in both children (see above) and adults exclude viewing events on a screen as a cause, this is somewhat controversial1 and doesn't exclude the possibility of the child believing he was really threatened with injury by the experience. Also, full-blown PTSD is not required for there to nonetheless be negative outcomes from repeated overwhelming situations..
Joaquín A. Mora-Merchán, Coping strategies: mediators of long-term effects in victims of bullying? Annuary of Clinical and Health Psychology, 2 (2006) 15-25
Note: 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.
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.
Maia Szalavitz, How Terror Hijacks the Brain TIME Magazine, April 16, 2013
Claim: "if the cortex shuts down and the limbic system or 'reptile brain' are left in charge":
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.”
Bessel van der Kolk, Posttraumatic stress disorder and the nature of trauma Dialogues Clin Neurosci. 2000 Mar; 2(1): 7–22.
Claim: "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.
Claim: "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.
Mariam Arain et al., Maturation of the adolescent brain, Neuropsychiatr Dis Treat. 2013; 9: 449–461. Published online 2013 Apr 3. doi: 10.2147/NDT.S39776
Claim: "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