There may be, but writing a 25 line perl script to do it would take less time than finding an application. I don't think you'd need to have a computer on all the time. (Although wouldn't the person doing the sorting have his computer on?) You should be able to extract receive dates from the emails themselves (not the send dates, as they can be wildly wrong).
Of course, all of that depends on access to your email server via IMAP, and I kinda get the impression that that might not be something that your company allows.
Try this: Open a Command Prompt. Type "telnet your.mail.server 143". If it connects, try typing ". login username password". You might have to put doublequotes around your password. If that works, you're golden. If not, try "telnet your.mail.server 993". If it connects, just disconnect; this is an encrypted session and you won't be able to deal with it manually, but the fact that it answers is a good sign. If neither one connects, you're back to looking for an Exchange-specific logger.
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Bitt Faulk