Lord Dattatrey incarnated in Satya Yuga[1] and maintained that form eternally. Similarly, Lord Sripad Srivallabh, the reincarnation of Lord Dattatrey maintained his Divine grace on earth fulfilling the wishes of his devotees even after taking samadhi. Later he reincarnated himself as Lord Narasinha Saraswati. The devotees still experience the divine manifestation of this later incarnation.
The incarnation of Lord Dattatrey never ends. For the welfare of the devotees He manifests Himself on any occasion and in any form to shower his Divine presence and grace. Hence the incarnation of Lord Dattatrey is eternal and everlasting.
[1] Satya Yuga: The Satya Yuga, also called Sat Yuga, Krta Yuga and Krita Yuga is the “Yuga (Age or Era) of Truth”, when humankind is governed by gods, and every manifestation or work is close to the purest ideal and mankind will allow intrinsic goodness to rule supreme. It is sometimes referred to as the “Golden Age.”
The yugas are said to succeed each other almost endlessly. After the perfect Satya Yuga, a decline marks the Treta Yuga. Further decline brings about the Dwapara Yuga, and after it comes the final and dark Kali Yuga, a time of wickedness, when man kills man. At the end of the cycle a Divine Being is said to take birth and reestablish righteousness, thus beginning a new Satya Yuga. Amongst the four eras, the Satya Yuga is the first and the most significant one. This era extends up to 1,728,000 years. Knowledge, meditation, and penance hold special importance in this era. All the pillars of religion are present in totality. During Satya Yuga, all people engage only in good, sublime deeds.