I got some advise from apple customer care. According to the very polite person, I was told that this was the FIRST time somebody reported to loose his sent mails! Hard to believe, but as I never would believe that somebody is lying to me, the only conclusion is, that Apple customer care is quite "distributed".
The advise was to make a backup of the IPad, delete and recreate my mail-account on the IPad.
Some interesting things I found with the Apple supporter:
When trying to "reproduce" the problem, everything works!
I have sent some mails with attachments to and from an other POP-Mail account and then downloaded the mails to my laptop what deletes the mails from the mail-server. Did this a couple of hours ago and I still can see the mails including attachments in Inbox and sent folders. I read in this thread, that it takes between 12 and 24 hrs for the mails to disappear. So I have to wait to verify.
My actual IOS is 9.0.2. The update did not recover the "not yet downloaded" ones.