If my wife conceives at age 34 and gives birth at age 35, then is that considered an at-risk pregnancy?

Premature birth: At-risk pregnancy is when there are conditions threatening the pregnancy which may lead to premature birth voluntarily or involuntarily . Your child was born premature and the pregnancy is over. Hope this helps to clarify your thoughts.

Loose term: The words "high risk" are imprecise and just suggest higher statistical risk of some negative outcome.Any pregnancy has about 4% risk of a surprise outcome. A woman's risk of a Down syndrome birth increases every year after the early 20's ; at 40 it hits an added 1%.Any health issue or pregnancy complication can be used to designate someone high risk.The term just reminds the staff to be on alert.