Please check if your library account is locked, e.g. because the annual fee is due. Please contact your library directly.
The Onleihe does not store your login data, but passes it on to the library software of your library. There it is checked if you are a valid user of the library. If that is the case, the login in your Onleihe is successful. Therefore, If you have problems with the login, you should always first contact your library.
It is quite possible that different libraries from the same consortia use different library softwares. This can mean that you can log into one library, but not in another from the same consortia.