If they were going to bring 300k+ forces in the 4th battle of Changsha, why did they think they would be able to take the city three times in a row with numerically smaller forces? Why didn't they just wait until they had gathered a larger force before attacking instead of wasting their forces in futile engagements? Did the IJA gain anything from their failed attempts at taking Changsha? I mean you'd think after the first two times they would have learned not to do the same thing over again. Was the IJA so ineffectual that it took them three tries before coming up with the idea of gathering a larger attack force?
Firstly, numerical superiority is relatively irrelevant in terms of actual combat. The Japanese army may have been numerically inferior to Chinese troops, but the rapidly mobilized and often irregular Chinese units had less firepower and combat value on a per capita basis than the Japanese troops. Japanese troops were generally better led, better equipped, and better organized than any Chinese unit, with the possible exception of the elite German-trained troops that had been bled severely in 1937 and were thereafter held as a strategic reserve for the duration of the war.
However this material superiority came at the cost of requiring vast amount of replacements, air support, and most importantly, logistics. Simply put, the Chinese required less supplies to wage war than the Japanese did, and their supply lines were far more secure and far shorter than those of the Japanese near Changsha. If you look at the terrain of Changsha, there are only really two routes of supply-by road/rail (which was already poor in China, and worse after battle damage and heavy partisan activity), or by river down the Yangtze --> Xiang river. This approach was extremely vulnerable as the Chinese controlled the other side of the river, and often could (and did) launch multiple raids to destroy or steal supply transports.
As a result of these logistical difficulties (on top of the sheer logistical failures of the IJA in general) it was difficult for the Japanese forces to fight at full capacity, or for that matter to bring 300,000 troops to bear. To do so would also involve a substantial commitment of Japan to total war, which Japan explicitly wanted to avoid in China as Japan's military was not meant to sustain a long total war, especially in a Chinese quagmire.
To define each attempted Japanese attempt to take Changsha, there was certainly a logical reason for attack with the forces that they did:
1st: After capturing Wuhan, in order to move towards the wartime capital of Chongqing, Changsha needed to be captured to allow the use of the river as a logistical supply route. Given apparent Japanese successes, it was not seen to be a problem to take.
2nd: This time, the army has been prepared better to attack Changsha, and has more up to date equipment.
3rd: This was initially meant to be a pinning attack, but initial success led to a follow-through attempt that ended... poorly.
4th: This was part of the last-ditch "Ichi-Go" Offensive, which essentially consumed all of Japan's strategic reserves for a hopeful blow to drive China out of the war. Though it was operationally successful, it was a strategic failure, and the Japanese offensive eventually broke down and collapsed as it was unsustainable and the spearhead troops were blunted and rendered combat ineffective for the rest of the war.