The SMTP protocol is very robust. As long as every link in the delivery chain is following the specification and there's no hardware failures, no message should ever be lost. One of two things should happen - the message will be delivered, or an undeliverable notification (bounce) will be sent to the original sender.
That said, not everybody runs a compliant mail server - especially in the age of spam, when all kinds of tricks are employed to thwart the inbound tsunami of unwanted mail.
My guess, based on the fact that you got a message a few days after it was sent, is that the messages were queued for delivery by his outbound server, and for whatever reason, that server couldn't forward the mail any further for a while. Could have been because the receiving server for your domain was down or otherwise unreachable for a period of time, or the server that his service relays mail through was down, etc.
The interval between retry times for mail delivery typically increases as more time passes. For example, if the message can't be delivered immediately, the sending server might try again 5 minutes later. If it still can't deliver the message, it might try 15 minutes later. Then 4 hours, then 12 hours, etc. After a certain amount of time (typically 4 days), the message will be deemed undeliverable and returned to sender.
If, after about 5-7 days, you still haven't received them and he didn't get any bounces (he should check his spam folder, too, as bounces are very often mis-categorized as spam), then you can figure that they got lost somehow or discarded. When that happens, it's always due to one of two reasons - hardware failure or a server being configured in a way that defies the SMTP specification.
None of that probably helps, since all you want is the messages to come through, but at least you (hopefully) have a better understanding of how e-mail works!
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