You have contacted me even though I did not expect a replay from you. You are a true gentleman. Please remember that.
In the age of instant communication, it just gets difficult to answer multiple e-mails. In my job, I can have over 50 e-mails waiting for me when I arrive at work. Its not an easy task to answer e-mails.
You can't keep up. I would say do your very best, and that is all anyone can expect. An auto reply might help. Perhaps a statement saying because of volume of e-mails, you might not be able to respond.