Research has suggested children who sleep on old mattresses during the first year of life are more at risk of developing breathing disorders such as asthma.

A study by The University of Auckland showed that wheezing at ages 3.5 and 7 years was more common in children who slept on a used mattress in the first year of life. Children who were treated with antibiotics or spent time at daycare in the first year of life also showed signs of breathing problems at 7 years old.

http://www.sciencealert.com.au/news/20072211-16625-2.html