Mechanism
Why wouldn't a militant power-seeking group create their own government by force, thus ending anarchy?
In 1918, the Treaty of Brest-Litovsk gave Ukraine from Russia to Germany in exchange for peace -- this ended Russia's part in WWI. Ukraine wasn't happy with that arrangment, however, and revolted to form their own anarchist state. Between 1918 and 1921, Ukraine was a functional anarchist community. Despite the lack of governmental authority, however, the people of Ukraine formed an army to defend itself against foreign aggression. This is the answer to your question: an anarchist community unites in defense of the community against militant groups who would seek the destruction of the community. However, Soviet militants overthrew this regime and in 1922, Ukraine became part of the USSR.
Anarchy depends upon people living their lives and ignoring the will to social power and the ability to subjugate their neighbors. The proletariat seems the only class capable of this, which is only to be expected, as they are the only class that actually struggles to survive and has no time to ******** around in the affairs of others. Anarchy is weak for the same reason communism is weak:
people suck.
Mechanism
In everyday life, why wouldn't the stronger and more violent people abuse the weaker?
Is that how it works now? To a degree, yes. This would not change in an anarchist community, because the same folkways and social mores still apply; however, the key to the system is having everyone voluntarily respect these mores. We call the violation of these mores laws; in an anarchist community, it is still a crime, but no Government enforces it.