Established in the Teaching
Svaniṣṭhā (literally 'standing in one's own [teaching]') describes the state of being firmly rooted in the specific doctrine and practice as transmitted by the guru-paramparā. For Sri Vaishnavas, this means being established in Vishishtadvaita as the correct understanding of Brahman, ātman, and the world, and in prapatti as the appropriate path, without mixing in elements from incompatible schools.
Not Mere Conservatism
Svaniṣṭhā is not intellectual rigidity but a fruit of genuine understanding. One is established (niṣṭha) in the teaching because one has understood it deeply through vicāra (inquiry), śravaṇa (hearing), and manana (reflection), and because the ācārya's authority and the śāstra's testimony have produced settled conviction. The alternative — dabbling in multiple philosophies without commitment — is seen as spiritually destabilizing.
Piḷḷai Lokācārya's Teaching
Srivachana Bhushanam discusses svaniṣṭhā in the context of what the ācārya imparts: the disciple who truly receives the teaching does not continue to shop for alternate views. This does not mean closing one's ears to other schools but rather that once the correct understanding has been received and internalized, it provides a stable ground from which other views can be examined without being disturbed by them.
Relationship to Prapatti
Svaniṣṭhā after prapatti means: having surrendered to the Lord through the ācārya's mediation, not taking back the surrender by trying to find other means or by creating new strategies for self-protection. The prapanna's svaniṣṭhā is their unwavering reliance on the Lord's promise of protection.