I disagree. I think he did some of his best work in season 3. In the first episode alone, he hardly had any lines, but conveyed so much with his face and his breath! Or what about the episode at Helwater? Just the look on his face when he left Willie broke my heart! For most of the first half of the season, he played Jamie as a shadow of himself, taking on various disguises and identities (Dunbonnet, Mac Dubh, Mac, Alex, A Malcolm) because he can't face being himself without Claire. When Claire returns he has to return to himself and reconcile it with the various other identities that he's had over the years.
Actually, I think he did some amazing work in the reunion. Watch the clip where he hears Claire's voice. He's facing away from the camera and we see his head perk up as soon as he hears her. He tenses up as she says "It's me, Claire" and turns around very slowly. He looks up at her with suspicion, like he's pretty sure it's a dream or a hallucination, and then the complete naked shock when he sees her. Then right into his graceful faint.
https://www.youtube.com/watch?v=linAZA1mKhU Again he had no lines, but he proves that he's such a physical actor that he doesn't need them. When we see the scene from Jamie's angle we see a certain alertness come into his eyes as soon as she says "It isn't Geordie."
https://www.youtube.com/watch?v=lDpSyofwlug He seems to almost choke on her name the first time he says it. We get the sense of awkwardness of the meeting when he starts to take his pants off in front of a woman that he hasn't seen in 20 years, but also still sensing the intimacy they once had.
He brings that kind of care and attention to all his scenes on the show, which is what makes Jamie work as a character. And if Jamie doesn't work then the show doesn't work because we need a sense of why Claire is so invested in him. But a lot of that is subtle work, and not as showy as a lot of the nominated performances. I also think that some awards bodies see Jamie as a stereotypical romantic hero and don't think that's worthy of recognition. I disagree, Jamie's a much more complex character than he seems at first glance. But I think that's why he doesn't get nominated.