While I don't have a citable reference from scripture, I have heard Sri Natteri Rajagopalachariar - Asthana Vidvan of Srimad Andavan Ashramam in a lecture state clearly that it is not possible for an Acharya to perform Sharanagati for a departed soul.
I will try to find a link to the audio lecture and provide it here.
On a different occasion, he has said that in the past, Acharyas were more strict about accepting a request for Prapatti and they would ask the devotee requesting for Prapatti to do some act to indicate their seriousness. Some examples:
- Asking a devotee to come again a few days later and repeating this a few times.
- Asking a devotee to go to Thiruppullani Kshetram and do Sethu snaanam (ocean dip) before Prapatti.
- Asking a devotee to go and participate in the Vedanta Desika Malai Utsvam in Thiruvahindrapuram
Once, a devotee requested Therazhundhur Andavan (who lived in the first half of the 20th century) to perform Prapatti. Andavan asked him to come a few days later. That person went home and died later that day. When Andavan heard the news, he was deeply affected by it and remarked that he had erred by refusing to immediately perform Prapatti for a jivatma who had spent millions of lifetimes to reach the current life. He wondered when that jIvatma would get another chance. From this anecdote, we may infer that it is not possible to do Prapatti to someone after their death.
Source: Natteri Rajagopalachariar's lectures on GuruParampara found here. The story of Therazhundur Andavan would be found sometime after lecture 90.