There is evidence both for and against the idea of a critical period. For example, Bowlby suggested that there is a critical period for forming an attachment, which is from the age of around 7 months to 3 years old. He suggests that if a child does not make an attachment during this critical period, then they never will. The idea of this is referred to as privation, which means that a child has never formed a bond.
Some evidence suggests that without forming an attachment in the first seven months, or during the critical period of up to three years, that a child will grow up to never form an attachment to anyone. An example of this would be the case study of Genie. Genie was locked in her room for the first thirteen years of her life because her father believed her to be mentally retarded. She never recovered socially or physically, and this suggests that as she never made an attachment, and got to past the critical period age, she never can form an attachment.
However, other evidence, such as the story of the Czech twins proves otherwise. The Czech twins were neglected and abused as children, and never formed an attachment with their parents. When they were found, they were taken into foster care by social services, and were later adopted by a new loving family. The twins formed a perfectly healthy attachment with their new family, and went on to have above average intelligence, and both had normal social and intellectual functioning. This suggests that the effects of privation can most certainly be reversed, and it is not at all down to the critical period to form an attachment.
In my opinion, I believe that the critical period doesn’t exist. If a child was to not form an attachment with the caregiver in the first three years of life, due to whatever reason, there should be no reason why they cannot go on to form a healthy, normal attachment to somebody else later on in life.