Doesn’t really feature in big games, does he?
Bruno Fernandes is a team player. His best performances are tied to good performances by the team mates. He's no Ronaldo or Messi, to solve things by himself (although sometimes he pulls off a rabbit from his hat). Agains't bigger teams, the team is dominated/controlled, so he just can't perform as well. And us being defensively frail, just undermines the attacking process too.
The Man City player who has the ball, always has at least 3 more team mates positioning well to receive the ball. Each Man City player looks dangerous and knows what to do with the ball and they all move with coordination and not dwelling too much with the ball. When it's Man Utd with the ball, you can see how sometimes they just feel lost about what to do with it, having to pass to the sides and back. I bet Bruno's performance, if he was on Man City's team, would be much better. And De Bruyne would struggle in Bruno's shoes...
I don't think Bruno lacks any stamina or that he needs rest. He just has to manage better his efforts. He tries to defend, to press the adversaries, to help the team mates everywhere in the field... If he just sprinted to press the oposition player with the ball, it''s natural if someone passes him the ball 10 seconds later, he won't be ready/able to sprint with the same intensity again. Probably will try a through ball instead of running with it a little bit further so that he won't have only one or two marked attacking options to pass to.
Anyway, if we depend on one guy to make things happen, we will always struggle agains't good teams.