TL;DR: Because the Yuan, Ming, Qing, and Communists found Beijing more feasible as a capitol and they happened to be the longest lasting regimes in Medieval to Modern Chinese history.

You're on to something when you say it's almost nonsensical. There are various perspectives to have on this, but I shall assume one from Inner Asian Studies, using the classic (and slightly outdated) Perilous Frontier by Thomas Barfield. I actually really enjoy this question because answering it requires explaining trends across several dynasties in China. Be aware, this is a very complicated answer, because it almost didn't become the capitol.

Barfield gives a very (over)ambitious model for Steppe nomadic and Chinese international relations and stability throughout history. The gist of it is this: horseback riding nomads formed steppe empires around the time when China united because of the riches they could acquire from raiding or trading with China. When a Chinese empire failed, the nomadic empire failed along with it, and in the power vacuum, Manchurian nomads could move in and form empires. Notably, the Mongols were an exception (we'll discuss this later).

Now how does this relate to Beijing? Well, southern China was typically the center of Han Chinese based empires with most of industry and economic production occurring there. So Nanjing was often the capital, taking advantage of that position. For steppe nomadic based empires, the calculations were different. Their center of power lay in the steppe (or Manchuria) and having a capital where they could both maintain presence to their nomadic homelands and power in China was key.

Now let me describe the narrative Barfield provides. From the 900s to 1200s, the key players in Chinese international politics were the Song dynasty in the south, and the various Conquest dynasties in the north (Khitan Liao, Jurchen Jin, Western Xia). The Jurchen were Manchurian based nomadic people, and according to his model, this means we are in the portion where the Manchurian based empires are possibly going to dominate. When a Manchurian based dynasty arises, according to Barfield, they will have a deep understanding of the steppe and typically send out disruptive missions to maintain steppe disorder, to prevent a challenger steppe empire from rising. The issue is that the Jurchen Jin were up against Temujin, also known as Genghis Khan, who against all odds prevailed and created the Mongol Empire. Barfield supposes that the Mongol success in such an adversarial environment led them to have unusually exceptional organization and boldness that helped them conquer most of the known world. For our purposes they were the first nomadic empire to properly try to conquer all of China, as opposed to taking parts of it near the frontier. The Mongols, after conquering the Southern Song, made their capital in Beijing, for the reasons I stated above. It was close enough to the steppe to maintain close relations to their homeland, and was also close enough to China to reap the economic benefits, though it was not easy to maintain as a capital. Beijing was not able to sustain itself through winter, even before becoming an imperial capitol, which necessitated a constant imperial guard and retainers that put even more strain on its meager resources. To sustain Beijing, the Grand Canal needed to be maintained, providing food and resources through winter, crucially acting as the artery from southern China to northern China.

But the reason Beijing is the capitol does not end here. For that we must look to the Ming. Barfield notes that after the Ming drove away the Yuan, the Mongols did not cease to exist. For the Ming, the Mongols represented a perennial threat, as they claimed authority from the Steppe. Now, the Ming dynasty crucially also made Beijing the capitol, because in an ensuing power struggle the then Prince of Yan, later to be known as the Yongle emperor, launched a campaign south from his territory: Beijing. In the campaign, Nanjing's imperial palace suffered heavy damage, and for Yongle, he made the crucial calculation that rather than rebuild the palace in Nanjing, he would move the capitol to Beijing, his seat of power which was also near enough for Yongle to keep an eye on Mongol challengers to the dragon throne. This decision is admittedly short sighted, as Beijing is directly in the line of defense in the north and the later Mongolian peoples actually captured Beijing in a subsequent Ming emperor's reign.

When the Ming weakened, the Manchurian peoples in the model under Nurhaci unified and began to self govern. After the brutal Ming-Qing transition, the Qing found themselves in control of China and faced yet again the same calculations other nomadic empires before them, that they needed to maintain a base near their homelands and the south, so Beijing was natural.

Perhaps the final element was that when the Communists undertook the Long March they maintained their bases and support primarily in the north. With Southern China wartorn from the Second Sino-Japanese war, and a historical capitol in the Communists hands, they found it more feasible to settle with Beijing as their seat of power.