I have an iPhone 5 running IOS 7 that is connected to my company's MSFT Exchange server. I get email without a problem, send without a problem and with 1 exception, actions taken via desktop Outlook replicate to my iPhone and vice versa.
Yesterday I received an email(small, no attachment) from someone that occasionally sends me email. I deleted it on my phone and didn't have any problem. About 45 minutes later it reappeared as an unread email. When I open it, it says "The message has not been downloaded from the server". It is deleted from Outlook and I emptied the trash folder.
This loop has been repeated a dozen times. I reset the phone, turned off mail syncing to no avail. My last resort is to delete the account and re-create it but I'd like to avoid that as it's a hassle.