I have worked with children ranging from ages 2 to 10 who were suffering from asthma. In many cases the older children had begun to exhibit asthmatic symptoms as a toddler and throughout time the severity of the symptoms had increased. In 50% of the cases the mother had been given antibiotics a few hours prior to the birth of the child. In other cases the child and taken several rounds of antibiotics due to ear infections or other illnesses. Antibiotics kill both harmful bacteria as well as many of the beneficial bacteria which support the immune system and colon health.
The lower count of good bacteria in a child gives way to internal fungus growth. The development of this fungus is also known as candida infection. In some children this increase in fungus can develop the symptoms of asthma. Along with asthma a number of these children tend to suffer from constipation. Old fecal matter and the toxins the body absorbs can also exacerbate asthma symptoms.
The nutrients I suggest are probiotics (can open up tablet and mix in some warm water and have the child sip through a straw). One capsule of at least 30-50 billion bacteria count can be taken per day on an empty stomach. About 3-4 months of supplementation is needed. Additionally a glycinate liquid magnesium will eventually ease the constipation (300-400 mg per day for about 10 weeks).
Fungi thrive on sugar so I also suggest lowering the amount of sugary foods and pastries as much as possible. Fruit juices are high in natural sugars so diluting the juice with water is a good idea.