Outlook user gets intermittent mystery bounce messages when replying to emails

I have been beating my head against the wall for nearly 2 months now over this issue.

We have a user that gets mystery error messages sometimes when sending emails from Outlook.  The error message comes from "System Administrator" but is not being generated by the mail server.  It contains the following:

            This message could not be sent. Unknown Error. Try sending the message again later, or contact your network administrator.


Diagnostic information for administrators:

Error is [0x80040401-0x80040401-0x000003ee].
Transport-Send failed: failure enum(25), HResult(0x00000000), EC(-2147220479).
Transport-Send failed: failure enum(22), HResult(0x00000000), EC(-2147220479).
Submit-Message failed: message id(51), failure enum(13), HResult(0x80040401), EC(-2147220479).

The problem only affects this one user.
It happens on two different computers that this person uses.  No-one else uses those computers.
Both computers are running Windows 10 and Office 365 (Outlook 2016).
The user sends about 150 emails a day and this problem seems to only happen for 1 or 2 minutes at a time and affects all of the emails that they try to send during that time.  It seems to happen about once or twice per day.
In all of the bounce messages that I can recall, at least one of the recipients is a user on our local domain.  I have not seen this happen on an email that was only to people in other domains.
It is not always the same person or people that are the recipients.
All of the bounce messages that I can recall were replies to messages, it doesn't seem to happen on new emails.
Our hosted-exchange provider (RackSpace) has confirmed that the error messages are being generated by Outlook, not their server.
If I open the bounce message in OWA, the text of the error is not there, but I can click to re-send the original message.  When I do that, the message goes through fine.

This is what I have done so far, with no effect:
Updated to the latest version of Windows 10 and Office 2016
Run a Quick Repair and subsequently a full repair on the office installation
Deleted the OST file
Deleted the profile completely and re-created it
Switched both computers to be a wired ethernet connection
Switched Outlook to only download the last 6 months of email
Deleted the Recipient Cache

Looking for any other paths to follow.  This user has been very patient, but that will not go on forever.
Christopher BeaugrandCIOAsked:
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Robert OrnelasVP Operations at Cook's ComputerCommented:
One thing i learned to check lately is if the user has maxed out their offline files cache limit. If you have offline files enabled check the cache.
Christopher BeaugrandCIOAuthor Commented:
Thanks for the comment.  Offline files are not enabled.
Robert OrnelasVP Operations at Cook's ComputerCommented:
Have you disabled any outlook addins if any.
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Christopher BeaugrandCIOAuthor Commented:
There are no addins.  Thanks.
Are there any disconections from the Network in Event Viewer
Christopher BeaugrandCIOAuthor Commented:
I don't believe so, though that's why I switched from WiFi to Ethernet.  But I will check the event viewer for anything that happened at the time of the last issue on one of the computers, which seemed to last for about 2 minutes.
Christopher BeaugrandCIOAuthor Commented:
I just checked all of the Event Viewer logs, and there was nothing at all recorded at the last time that a bounce happened.  No errors, no events at all.
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