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]
(..) The tether... it disengaged itself from the system and then reappeared... some kind of glitch. It's entirely unnecessary to maintain her tether. All that matters is that she arrived. Hey! Tell him what you did. Clearly, Dr. Railly hasn't done anything yet. There's still time to bring her back. (..)2016 TvShow: 12 Monkeys Title: Lullaby Season: 2 Episode 8