It depends on the presence of other substances that bind to the absorbent. If part of the binding sites binds something else than dye and that this binding is irreversible, it will lead to a gradual decrease in the number of available bindings sites. You may need to look at what is present in the feed stream and next pick an intermediate cleaning step that will remove also those substances.
How do you separate the adsorbent from the solution?
By filtration you will lose part of the adsorbent after each cycle.
Seems like you have a systematic decrease that might be explained by a systematic loss either in the adsorbent capacity as Mr. Vleugels explained or the amount of adsorbent.