This is a very interesting questions and unfortunately, as this is always the case in science, we can find different values in literature, ranging from 2 - 15 hours.
I hope, some more experienced colleague can shed more light onto this question.
I've attached some files and URLs, where I found these data.
Thank you so much for your prompt response and for the links. It really looks like it is a difficult question to find the answer for. From what I understand from the links you suggested, it seems as the half-life of IL-6 is somewhere between 2 and 6h. The 15h suggestion is based on an in vivo response and there is probably a sustained production of this cytokine.
You're welcome Giorgio. And yes, you're right. I forgot to mention that half-times may vary between any experimental condition one chooses. I would also say that cytokines shouldn't have a very long half-time, especially in the case of IL-6, because of its pleiotropic effects.