I kind of fixed my problem a little bit... maybe yours too?
In some other forum I have read about DHCP issues and investigated a bit further.
The freshly booted Kobo got two different IPs for the same MAC addresses, which is kind of odd. I suppose it sends out two DHCP request in quick repetition. See attached screenshot from the router webpage. Also the 255 address is strange, because (depending on the subnet size) it should be for reserved for broadcasts (?)
Now, I have set the DHCP to always assign the same IP address to this MAC and rebooted the router to get rid of the current double allocation. Good thing is that it correctly receives one IP address now, bad thing is... it solve the problem only a little bit. After sleep mode the stupid "There was a problem ... please try again" message is still popping up. BUT, trying it again actually worked! Without a reboot.
Maybe other routers are a bit more fault tolerant against the double DHCP request? Or answer quicker to avoid a second request.
Credit where credit is due: This guy had the same idea already in 2011
http://www.lesen.net/forum/ebook-rea...ten/#post42126 (if you can read / google-translate german)