The period of attachment only happens while a child is young. However, as he grows older, the amount of time spent with his parents will decrease as will the strength of the attachment between the two. During this time, he will be out with his peers or at school a majority of the time where he will be influenced by those around him. Individuals who grow up without a secure attachment to his mom may develop a good relationship with another individual whether it be a peer or an adult that can result in a good well-being later in life.
Another point is that while some children develop secure attachments with their mom and display these during tests may not grow to be more attractive towards other peers. Children with autism may display signs of secure attachment due to their higher comfort level around adults. However, when they are put into an enviroment with children their age they are unable to create the peer-peer relationship. While these children display secure attachments, they will not develop to have the same well-being later on in life.