Hello! I asked this question a few years ago and got some terrific responses!

Here is a slightly modified version of an answer I wrote on r/history a few months ago:

First and foremost, there are multiple instances in Indian history where an entity based in North India was able to project its power into the south, and also vice versa. The early Company Raj, based at Calcutta in Bengal, was able to project power both westward into the interior Gangetic plain and southward into the Northern Circars and Carnatic coast of modern-day Andhra Pradesh and Tamil Nadu. British Indian armies marched along the breadth of India from South India to Bengal long before the introduction of the railroad. Pretty much the same route was also taken by the Guptas some 1400 years before, whose armies (if we are to believe Samudragupta's Allahabad pillar inscription, especially Lines 19-20) advanced as far as Kanchi in Tamil Nadu, as well as by the Cholas, as described in Tamil sources like the Kalingattuparani. The armies of the Delhi Sultanate during the early 14th century overran virtually all of South India, as did the Mughal armies during the late 17th century.

The main difficulty in creating a pan-Indian empire was not projecting power from the Gangetic plains into South India, as there were no serious geographic obstacles separating the two macro-regions. The Vindhyas and Ghats were never impassable like the Himalayas, and did not feature sleet or snowstorms (the bane of many pre-modern armies) as in the Hindu Kush mountains. If an empire based in North India wanted to exercise domination over South India, the major obstacles it faced were not primarily geographical but rather political in nature, especially the inability of many historical Indian states (both Hindu and Muslim) to effectively control their own subordinates and maintain territorial cohesion. For instance, just a few years after the Delhi Sultanate invaded and conquered the Deccan and South India, the governor of Madurai in southern Tamil Nadu, Jalaluddin Ahsan Khan, declared independence from the Delhi Sultanate and established his own independent state (Madurai Sultanate). The governor of the Deccan also declared his own independent sultanate (the Bahmani Sultanate) in 1347, and as the Delhi Sultanate continued to weaken, independent sultanates also appeared in many other regions such as Bengal, Gujarat, Malwa, and Jaunpur, so it wasn't simply an issue with South India. Likewise, the later Mughal empire was able to temporarily conquer almost the whole of South India, only for the empire to disintegrate soon after Aurangzeb's death in 1707 with the various nawabs (governors) becoming de facto independent rulers, not just in South India but also in provinces like Awadh in the Gangetic plain. It was the British who finally ended this pattern in the 19th century by introducing centralized, bureaucratic governance of the entire subcontinent for the first time in its history, with every district of British India being governed by a salaried civil bureaucrat (District Collector) rather than by what amounted to a bunch of miniature kings with their own private armies who were prone to revolting at any time.

To summarize, there was nothing unique about South India that prevented empires based in North India from invading and conquering it, which they did several times throughout history. The problem was actually keeping it bound to the central government (in Delhi or wherever) after the initial conquest, and here North Indian empires failed because of underlying issues in their own political system. North Indian regimes encountered these same issues outside of South India as well, but they were amplified in South India due to its greater distance from the central authority. In other words, geography aggravated underlying problems that made it nigh impossible for a stable pan-Indian empire to exist prior to the British Raj, but geography itself was not the decisive inhibiting factor. If it was, then the British in the 18th and early 19th centuries (before modern technologies like the railroad and telegraph allowed central governments to greatly overcome traditional limitations of space and time) should have failed just like all of the previous regimes that tried to rule India.