Lennart, thanks for checking and confirming this with your iPhone. Seems like apple don't want third party adaptors, they prefer to sell the expensive one themselves.
We have added a warning on sales page of the lightning adaptor we sell.
Hi, we heard from another customer that this happened when using the lightning to usb adaptor we sell, after the latest iOS update.
Do you have access to an original Apple lightning adaptor to try?
No, I don't have an original apple lightning adaptor to try.
A customer confirmed that the DAC works with the original Apple lightning adaptor with 10.3.1 (and not with the one we sell). We will add a warning about this on the lightning adaptor page.
You can return it for a refund.
Here is the original Apple lightning to USB adaptor: