Unlikely to be the cause. If the email can be sent, the address is functional. Ther "reply request" follows the same email back. More likely, they aren't sending the receipt, or their email account is not able to reply from the address that you have used. This can happen if, for example, I have two accounts one at bjh @ myisp.com and bjh @ my oldoutofdateisp.com If I had asked you to send me mail to the latter, while on line with the former ISP, the automated reply would be disallowed by my current ISP
You could test your own email by setting up a second email account and sending yourself a mail.
Sounds like a "their problem", not a "you problem" to me.