I see no point to the “Did you see my/her/his e-mail?” e-mail, nor its close cousin, the “Please respond to my/his/her e-mail,” e-mail. It is particularly vexing when received less than 24 hours after the original mail, and it’s downright annoying when received less than 8 hours after the original mail.
If I *did* see the e-mail, presumably, I’m working on responding to it. Perhaps I’m trying to gather information. Perhaps I’m waiting to confirm a piece of data. Perhaps I just want to let my thoughts settle to make sure that you get a good response. Either way, the e-mail is in progress. Sending another e-mail just means that either I have to ignore the second e-mail or spend time replying to it that could have been spent on the original task.
If I didn’t see the e-mail, there’s no guarantee that I’ll see this one. Thus, you’re better off just picking up the phone and giving me a call. This saves us both an e-mail.
The only reason I can see for this kind of e-mail is if the deadline for a needed response has been missed or has changed, or if the original e-mail wasn’t clear about who should respond (i.e., was sent to a large list, and the lead is now directing who should respond). (In the former case, I think a phone call may be warranted, just in case the original e-mail was missed or not received.)