Thanks a lot for your quick reply!
I initially had the red circled option disabled, but I enabled it
after people already had clicked on "complete" in their surveys.
After changing this option I tried again to resume and it failed with the same error message ("There is no matching saved survey."). I also tried without the resume mechanism/link by just clicking at the orginal URL sent to the participants. Then, I just land on the first page of the survey which I can start then, but all with empty answers (I cheched that there should be answers in the admin-interface).
In one survey, which cannot be resumed, the Uses left is =1 (I don't know whether that matters):