First that refers to the fact of the email having arrived safely "in the inbox". Second that refers to the fact that it hasn't been forgotten/overlooked in the inbox by the recipient, (would be confirmed by a "thank you" email) interpret "lost" as not seen by the recipient. Third that refers also to what was mentioned in the second "that" above. Forth that = that day = the day on which the sender sent the email. This is a case of the writer being over zealous with the use of the word "that' "a simple "thank you" to let the sender know that their email has arrived safely and has not been overlooked would be most welcome'' better and with only one "that" that covers everything.