There is various causes that leads to easy tiredness or fatigue in children. It can be due to heart related or can be non-cardiac.
Cardiac causes that lead to these symptoms are severe aortic stenosis, severe pulmonary stenosis, and severe coarctation of aorta. Due to these diseases, there is low cardiac output that leads to less blood supply to the body and leads to early tiredness.
Other reasons can be a busy schedule, not getting enough sleep at night and even being hungry can all make a child tired. But if a child is consistently feeling tired, tiredness may be a sign of an underlying problem.
Interestingly, school-age children do not usually complain of daytime tiredness or fatigue, even when they do feel a little tired. Instead, these concerns are more often noticed by a child's parents or caregivers. So when a child talks about being tired or shows obvious signs of fatigue, like lying down to rest in the middle of the day, for example, that should be taken seriously. It may point to an underlying medical condition that needs evaluation.
A variety of illnesses can cause a child to be tired. Most acute illnesses — for instance, upper respiratory infections like colds, or ear, throat or sinus infections — make children tired. But with these illnesses, the fatigue goes away when the infection clears.
More prolonged or significant tiredness could be a sign of allergies or asthma. Tiredness that lasts is the most common and prominent symptom of mononucleosis — often called "mono" — caused by Epstein-Barr virus. Fatigue that persists could also be related to poor sleep that results from a sleep disorder, such as obstructive sleep apnea.
Rarely, chronic fatigue may reflect a more serious underlying condition, such as tuberculosis, diabetes, inflammatory bowel disease, chronic kidney disease, heart failure, cancer or very poor nutrition. It also may indicate an emotional, educational or social problem.
As you mentioned, parents frequently bring up anemia as a possible cause of a child's tiredness. Anemia is a condition in which there aren't enough healthy red blood cells to carry adequate oxygen to the body's tissues. Tiredness can be a symptom of anemia. But unless it is quite severe, anemia is rarely the cause of persistent fatigue in children.
Cardiac issues need to address on emergency basis with early relief form stenosis or obstruction by balloon dilatation of the stenosed site.