Can our online personas live on beyond our deaths? Why or why not?

No - an online persona isn't much of a persona to begin with.

Many people put a facade over their true identity when online (or on social media) for any number of reasons. They try to create a virtual life of upbeat social interactions, appearing happy and seeming to live a great life. A person's true personality needs to be revealed through real life experiences with others.

After someone dies, nobody thinks about their facebook followers, quirky posts/comments online, or how many blogs they wrote; their smile, unique personality, and what they accomplished will live on in people's minds.