He 'kept/maintained his cool' [=he didn't get angry or upset] even though it was clear that he was being unfairly treated.
He was struggling to 'maintain his cool/composure'. [=he was struggling not to become angry or upset]
They barely had enough food to 'maintain life'. [=to make it possible for life to exist or continue]
(..) And I saw it with perfect clarity. I saw what my sins were. The gold I had, the wine I drank, the women I used, my ceaseless struggle to maintain my position. It was all part of a story. A story I was telling myself about who I was. A collection of lies that would disappear in the light. (..)2016 TvShow: Game of Thrones Title: Book of the Stranger Season: 6 Episode 4