Therapy is supposed to be talking about feelings to understand more what's underlying them and not reacting on them with actions. Being bored is a feeling too and the same treatment should be applied.

Of course, the client can terminate any time they want but from the therapist's side I personally would expect that any decent therapist would try to understand why he's feeling bored and try to use this analysis to help the client. The most typical textbook example is that the therapist starts feeling bored in counter-transference when the client is hiding something important. Surely there are other reasons, including those that are stemming from therapist himself, like for instance having some problems in his life that he can't put out of his mind and thus everything else sounds boring etc etc.

Anyway, referring the patient out because of that doesn't sound a reasonable option for me at all. Rather, the therapist should work on themselves to understand why they are feeling that way and if this is something personal then solve it so that it wouldn't interfere their work and if this is something coming from the patient, use that understanding to further the therapy. But it all starts from the self-knowledge of the therapist.

I have been with my T for four years and although I think he has been often frustrated I don't think he has ever been bored. Same applies to me.