I don't know. There's really no "normal" for how to handle investor relations. In this particular situation, I can't see any downside to regularly reassuring investors. Some companies do, in fact, discuss steep drops in share price and some don't.

Besides the costs of the time he spends answering emails, there's the time not spent on doing more important stuff, as a result. How about if he announces regular updates and at the same time announces he no longer will be answering individual emails?