According to the book "Hindu Dharma" by Sri Sri Chandrashekarendra Saraswati:
If the Gayatri has not been chanted for three generations in the family of a Brahmin, its members lose caste (they cease to be Brahmins). The quarter where such Brahmins live cannot be called an "agrahara". It is perhaps not yet three generations since Brahmins gave up the Gayatri. So they still may be called Brahmins.
In the same way if the Brahmin family has not performed sacrifices for three generations its members will be called "Durbrahmanas", degenerate Brahmins. Even though degenerate the label "Brahmin" sticks to them. There are prayascittas (expiatory rites) by means of which the corrupted Brahmins will be remade true Brahmins. But there is no such hope for a Brahmin in whose family Gayatri has not been chanted for three generations. A member of such a family ceases altogether to be a Brahmin and cannot be made one again. He is just a "Brahmana- bandhu", a kin or a friend of Brahmins. The same rule applies to Ksatriyas and Vaisyas with regard to the Gayatri mantra; they become "ksatriya-bandhus" and "Vaisya-bandhus" respectively.
Now, technically I am a Kshatriya-bandhu since upanayana hasn't taken place in my family for more than three generations. So what are the duties prescribed for me? What about Brahmana-Bandhus and Vaishya-Bandhus?
Edit: A.C. Bhaktivedanta Swami Prabhupada in his commentary to Srimad-Bhagavatam 1.12.35, equates Brahmana-Bandhus to Shudras:
Simply taking birth in the family of a brāhmaṇa does not make one qualified to perform yajñas. One must be twice-born by proper training and initiation from the bona fide ācārya. The once-born scions of brāhmaṇa families are equal with the once-born śūdras, and such brahma-bandhus, or unqualified once-born scions, must be rejected for any purpose of religious or Vedic function. Lord Śrī Kṛṣṇa was entrusted to look after this arrangement, and perfect as He is, He caused the yajñas to be performed by the bona fide twice-born brāhmaṇas for successful execution. The unworthy sons of the royal orders are called kṣatra-bandhavas, as the unworthy sons of the brāhmaṇas are called dvija-bandhus or brahma-bandhus.
Does that mean Dvija-Bandhus have the same duties as Shudras? Should they be treated as Shudras as well or as the Varna they are born into?