In my experience, the most common reason for emails vanishing in the manner you describe is the mixed use of email client protocols. The 2 most common protocols are POP and IMAP (The MS Exchange protocols are very IMAP like)
Without more details on how the Secretary or Boss clients are configured, I would make the assumption that the secretary is using a POP-like protocol to collect email, and the boss is using an IMAP or exchange-like protocol.
POP is designed to collect, and then remove emails from a mail server. It is not designed for access from multiple clients.
IMAP is designed to either read emails from the server, or operate on a cached copy, but the email is left on the server so it can be accessed in multiple places.
So the boss will see a new email up until the point the secretary's system grabs and deletes the server copy.
If the above is correct, then possible solutions would be:
- (best) Migrate the secretary to use IMAP/Exchange protocols to collect email.
- POP can be set to leave emails on a server. This is not ideal, but may be sufficient.
NOTE: Please forgive the assumptions I've had to make in this answer. I would have added a comment requesting more info but I have insufficient reputation