The TV entertainer and actor was axed by his rivals, who thought that his "low points" were starting to have a negative effect on the group.
In the final vote, Richie and Andrew Castle both picked up three nominations and the final decision went to rugby star Gavin Henson, who won this week's immunity challenge.
Henson chose the EastEnders star over Castle, claiming that he wanted to give the former GMTV presenter a second chance.
"I thought Andrew felt like he let himself down yesterday," said the Welsh sports icon. "And in sport you always crave the chance to put it right. He's got that chance now."
Speaking afterwards, Richie said: "I think there was always going to be a point where age came into it. In my head, I'm still 22, but my body is telling me something different.
"Also maybe Gavin saw me as a bit of a threat. I doubt it, but it's at the back of my mind. I was the only person who went up against him twice and nobody else has beat him yet except me."
Andrew Castle, Gavin Henson, Susie Amy, Marcus Patrick and Joe Absolom are the remaining celebrities battling it out in Norway.
71 Degrees North continues on Tuesday, October 19 on ITV1.