So your question, like many on this site, is actually somewhat mistaken. Both the Mughals and the Delhi Sultanate controlled large chunks of South India at their peaks, although you're correct in that they only did so for a short period of time. I can't also can't really speak much on the Mauryan Empire, since that's outside of my field, but consider that your sample size here is basically 3 or 4 large empires that could have (or did) expand from North into South India: the Mauryan Empire, Delhi Sultanate, Mughal Empire, and the Marathas.

And the Mughal Empire is probably the best example among these to show that indeed South India was far from undesirable. Aurangzeb, the last powerful Mughal emperor, famously staked a significant portion of his career and much of his treasury on conquering parts of South India. At its maximum extent, Mughal power had reached almost to the very southern tip of the peninsula, but only after a hard-fought and deeply taxing series of campaigns. A number of factors, especially the stress of war, the ascendency of the Marathas, and Mughal infighting meant that after Aurangzeb's death in 1707 his empire would very rapidly lost control not only over South India, but most of its northern territories as well (though it would nominally remain in power). So South India was actually so desirable to Aurangzeb that he was willing to make massive sacrifices to conquer it. Also remember that around this time, European trading companies were arriving in India, and all three of the early ones (the Portuguese, Dutch, and British) prioritized South India for its wealth of resources.

I also think that your question largely answers itself. Southern India was rarely conquered by northern empires because they were situated in the north which, naturally, is very far away from the the regions that made up present-day Kerala and Tamil Nadu. It is therefore unsurprising that empires primarily based in the Indo-Gangetic plain and its surroundings would rarely, or briefly, control areas far to the south. It should also be noted that few empires in human history have controlled as much densely-populated territory as the two you mention in your question -- it was likely hard enough managing northern India alone.

In any case, the straightforward answer is not that South India was undesirable, or that it was especially good at defending itself from invasion, but rather that the usual historical circumstances that stop empires from endlessly expanding also apply here (logistics, resources, succession, factional politics, etc.). Looked at from another perspective, it is actually more surprising that several empires based in the north penetrated as far as they did into the south.