The Nimbus may only be an Earthican ship, considering the high concentration of humans on board. There are probably many more DOOP starships, and probably bigger ones too, but they defend other DOOP planets. Why the Earthican defences have to call on civilian craft to defend the planet is probably because the professional defence force keeps getting whittled down too quickly, and other DOOP ships from "abroad", as it were can't get back in time\ can't be arsed.
According to various sources either in the show or in the comics - which I suppose we could count as "cannon" - Earth gets attacked almost every week in one way or another. It's unlikely Earth has enough time to produce an effective defence force and its replacements in that time, plus they need to find pilots willing to join....
The Nimbus has probably survived since Zapp knows when to "keep out of harms way"
But he is the most decorated and regarded captain, which is why the Nimbus is assigned many different missions, and is why Leela keeps bumping into them.
Scratch that, perhaps there are lots of different DOOP ships, but they take it in turn to guard different places, so while the Nimbus is away, other ships will defend Earth, but when big invasion fleets come, Zapp will rush back to Earth to take all the glory - which is why the Earth Defence Force or whatever the hell you want to call it, is so small and why they have to call on civilians to fight, if you know what I mean
It's unlikely with a president like Nixon, that Earth will have a small defence fleet due to it wanting to appear a peaceful planet.