In Jain history, the Śvetāmbara gaṇas in South India did not remain a dominant, continuous monastic presence. Early Śvetāmbara tradition says some Jain teachers moved south during the great famine, and later Śvetāmbara teachers are mentioned in South India; but over time, Śvetāmbara monastic lineages there did not become as prominent as in western India. In South India, Digambara Jainism became the stronger surviving tradition, while Śvetāmbara activity gradually became limited or absorbed into later Śvetāmbara orders and lay communities. ( jainpedia.org)

So, in simple words: they did not “disappear” all at once, but most South Indian Śvetāmbara gaṇa traditions weakened, merged, or faded, and the Jain presence in the south became mainly Digambara. ( jainqq.org)

If you want, I can also explain this in the context of gaṇa, gaccha, and śākhā in Jain monastic history.