Are there members in people's ancestry who claim to have seen Jesus, or witnessed His acts? Historians/writers were able to get written accounts of Jesus's life and acts from the eyewitness accounts of people who had seen Him during His lifetime. It occurred to me that I have not seen or heard claims from people in this lifetime (or a few previous) stating that their ancestors met or saw Him, whether based on story passed down or diary/journal documentation. 

I know there's got to be an obvious reason, but I'm stumped on why not?
There are some families amongst the Ancient Churches of the Levant (Syria, Lebanon etc.) that do claim descent from particular apostles. For example, some members of the Semaan family claim descent from the Apostle Peter. Similarly for the families Andraos (Andrew), Hanna (John) and Matta (Matthew).