A customer hat the issue, that when a user booked a resource, the entry could only be modified the same day. If the user tried to modify the entry one day later, it was not possible anymore.

Error Message: You marked “Resource” as a resource. You cannot schedule a meeting with “Resource” because you do not have the appropriate permissions for that account. Either enter the name as a required or optional attendee or talk to your administrator about giving you permission to schedule “Resource”.
Error Message in German: “Ressource” wurde als Ressource markiert. Sie können keine Besprechung mit “Ressource” planen, weil Ihnen für dieses Konto die entsprechenden Berechtigungen fehlen. Geben Sie den Namen als erforderlichen oder optionalen Teilnehmer ein, oder varanlassen Sie Ihren Administrator, Ihnen die Berechtigungen zur Planung von “Ressource” zu erteilen.

Well, the problem was not a permission issue, the permissions were all set correctly.
Much more this happened due to the fact that the mailboxes were migrated to Exchange 2010 and were converted into resources that time.

To solve the problem you have to log in into the resource with a outlook client.
Options Calendar Options  Resource Planning  and uncheck the box Automatically accept meeting requests / Edit cancellations.