It sounds as if you have two different devices registered/authorized with different Adobe IDs,
or you got a book while under one ID, and then registered a different ID on the computer.
Please give more details about your computers and devices and how they have been registered.
Every Adobe DRM copy/loan of a book is associated with the ID of the device at the time the copy/loan was acquired.
It cannot be read on a device associated with a different ID.
Running a device 'authorized without ID' creates an anonymous/implicit ID that cannot be put onto any other device.
Also, if you change authorization on the original device, that ID cannot be recreated even on the original device.
Any book acquired under the anonymous ID becomes unreadable.