It seems that the problem was that alot of people accessed the account from different devices and from different applications (I think the access via unofficial applications was the main problem). The instagram-servers then flagged it automatically as suspicious which made it impossible to retrieve feeds via the public search-API. However, if you use your own token you can retrieve the posts from your side. Unfortunately instagram support needs ages to respond and they did not unflag the account when I told them that the behaviour is normal (maybe it is just not possible for the support to unflag an account).
Hope this helps if you ran into the same problem.