I think another factor not wholly covered by Keen is the mind set of the nations, and the associated benders.
Earth benders have a stubborn, passive defensive mindset. Perfect for resisting a siege but not counter-attacking.
Fire benders have an arrogant, actively aggressive mindset. Perfect for endlessly laying siege, but not defending.
I don't remember any group of earth-benders forming a resistance on the scale needed to defeat the fire nation. Anyone thinking like that was an outsider, with a slightly different mind set to the other earth benders. If Ba Sing Se had mobilized it could have flattened the fire nation, they just don't think like that.
The water tribes had already been harried soon after the suspected death of Aang, as they would be the next holders of the avatar. Also because water beats fire, so the fire nation wanted to close off that threat as soon as possible. Being so marginalised they would struggle to mount a direct offensive, as well as the fact they have a counter-attacking attacking mindset (think how Jiu-jitsu and Aikido work); to a water bender you never strike first.
The air nomads...I don't really understand how they think. Crazy hippies.
In short effectively taking out water and air left two nations suited to siege warfare, meaning that the fire nation were rarely threatened.