While one occasion of waking up at 3 AM and not being able to fall back asleep does not constitute insomnia, there is a type of insomnia that describes that type of poor sleep.

Sleep maintenance insomnia is a type of insomnia that describes difficulty staying asleep throughout the night or difficulty going back to sleep after waking up during the night or early morning hours.

Ellis, G. (2014, Jul 08). Recent studies link sleep issues, diabetes. Philadelphia Tribune Retrieved from https://search.proquest.com/docview/1549956226?accountid=14496