I'm using POP mail and had the same result with dialogue that the message was not downloaded from the server. Yesterday, I resent several emails to myself from another device and the photos in those messages arrived ok. I checked the device several hours later and found the attached files were still there. I then did an iCloud backup last evening and this morning I find all messages in the Inbox and Sent mailbox show nothing except a dialogue that the message has not been downloaded from the server. That proves my understanding that the issue was limited to message that were in mail at the time the upgrade to iOS9 was done was incorrect as this is clearly an ongoing issue with iOS9.
I am going to wipe the phone and do an iCloud restore from a backup that predated the iOS9 upgrade. That will restore all of the data on the phone except for anything added after the upgrade however it will not restore any email messages. If you decide to go this route be careful to copy any messages on the iPhone to another device or they will be forever lost.
Apple does not look at discussion forums so in order to get this directed to their attention use this feedback link: http://www.apple.com/feedback/iphone.html
If enough of us send feedback to Apple it will get their attention.
<Edited by Host>