It seems the land would be pretty easy to conquer and both China and Russia could easily just take some of it without much repercussion. Are there any diplomatic reasons for this or is it just because most of Mongolia's land is pretty much useless wasteland?
Mongolia was part of Qing China until 1911, but in many ways this was less direct than elsewhere in the Empire as there wasn't the same level of Sinicisation happening there as elsewhere in the Empire. As the Qing was falling during the 1911 Xinhai Revolution, Mongolia declared independence with a bit of support from Russia. This was short lived and by 1915 is lost its autonomy, and by 1919 fell under Chinese military occupation. Then in 1921 there was a revolution which got rid of the Chinese military presence, and after a bit more support from Russia, some level of independence was once again achieved in 1924, but as the Soviet-styled Mongolian People's Republic, and largely under the control of the USSR as a Soviet satellite.
Throughout this time it was still considered part of China by the Chinese government, up until the signing of a treaty between China and the USSR in 1945 that settled the matter as far as the Nationalists were concerned. Then in 1949 the Communist government, then taking power in China, recognised Mongolia's independence.
In the early 1990s with the end of the Soviet Union, Mongolia underwent reforms. 1990 saw a democratic revolution, and in 1992 they undertook constitutional reforms.
Right, so then the question of why it hasn't been reconquered.
Prior to the fall of the USSR, China lacked the military power, and if they had it would have likely been more focused elsewhere.
Russia meanwhile (prior to 1996, our 20 year rule marker) didn't need to take over Mongolia; it already did so by making it a satellite. Mongolia existed in the Soviet world and only in the Soviet world. Their foreign policy was entirely handled by the Soviet Union. Mongolia was for all intents and purposes part of "Russia".
Today with the USSR out of the picture, China would be in a much better position to do so if they wanted. However with the 20 year rule around here there's not much to be said about it. Both countries (Russia and China) would have plenty of good reasons for not attempting that anyway, which for the most part should be fairly obvious.
tl;dr: Mongolia was part of China since the 1600s, and a puppet state of the USSR after that. The premise of the question is flawed.
(edited for wording because it's late and this needed better proofreading before I hit the submit button)
Why do we say that Mongolia was a part of China? To me (a lay person), it makes more sense to say it was a part of the Manchu empire, and that Mongolia and China were separate and distinct entities in the same realm.