Emails in Outbox, can't delete them

One of our users' iPhones has been found to have lots of emails in the Outbox. I've seen this before with failed messages, but these ones also appear in her Sent folder. The phone is on iOS 9.1.

If I try to delete them, it complains that they can't be moved to what I think it called the "Rubbish Bin".

I turned on Airplane Mode, and was then able to delete them. However, when I turned Airplane mode off, they all returned.

Has anyone seen this before? Any ideas for how to get rid of the emails, and how they ended up stuck in there in the first place?

The mail account involved is for our company Exchange server.