Hi Eric,
Thank you for your response, I would like to provide some update for your reference.
First Office 365 ensure 99.9% uptime service level agreement which including all the running service, based on my experience, this is almost impossible that customer will encounter the missing email issues which is caused by Office 365 Server.
Also I would like to share some background that there're various reasons will cause an email missing issues. According to your post that you mention the email has been discovered in the sender's sent items folder, however, according to mail flow chart, the email still need to pass several sender's internal mail server hop or security gateway, then it can be delivered to internet. Also the internet DNS server, sometimes will also have the possibility to cause email has been routed to wrong destination.
So normally to trouble shoot this issue, we will do message trace to prove that email has been delivered to Office 365, then we can have the evidence with details which can help us to narrow down whether it's related to the Office 365 internal problem.
The difficulty part for this ticket is, at this moment, you cannot get the related message trace result, which we don't have the sufficient information to problem email reach Office 365 server and continue the trouble shooting.
However, to give some additional help, I think if you discover an email missing issue in the future, please try to trace the message as early as possible, then we can prove whether email has reached office 365 server. Also, can you let me know your domain name via private message, so that I can ensure the MX record (used to receive email) is correctly set which will not have any negative impact to your running business.
Look forward to hearing from you.
Cheers,
Pinko