Biggest monkey is boss monkey. Biggest monkey with most monkey friends is next boss monkey. Monkey friends only harass monkeys with no friends and suck up to the boss monkeys and their friends. It's good to be boss monkey. All the other monkeys have to regulate themselves or get ripped apart.

Aren't they constantly challenged and at some point inevitably lose due to injuries and/or age?

They can be stable for a few years at a time if there's lots of food, water, and decent weather, no injuries or major stressors. So yeah, boss monkeys don't stay that way forever, and it requires lots of work maintaining health and social relationships. The physical challenges are a function of pure physicality, there's no monkey jiu jitsu, it's all rage flailing - the fights are probably a lot less work overall then the socializing.