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]
(..) Your Grace! Don't want to overfeed them. Tomorrow perhaps. "And though Daenerys maintains her grip on Slaver's Bay, forces rise against her from within and without. She refuses to leave until the freedom of the former slaves (..)2015 TvShow: Game of Thrones Title: Kill the Boy Season: 5 Episode 5