The renew mail just came in.
Seems to be working this time, so the issue is solved for me.
Just some additional information for debugging purpose:
The "Uh oh, something went wrong" message appeared some seconds (~5sec I'd say) after I initiated the renew process, not some minutes after.
When this message showed up I instantly tried to restart the renew process some times (I think i did that 4 times), so maybe that had some influence on the instant expiry therafter.