Just a few thoughts, based on my understanding of Rowlf. He's a very laid back Dog, so laid back that he describes his life as nice and simple in TMM, he's in a hammock in The Muppets and he always describes himself as "the dog that plays the piano."
Now, as interesting (fun?) as it may be to look beyond that exterior to find that he's a hurting person inside...I've personally never felt that with him. Remember when he got left behind and chased the car all the way up to the farm house, then played the piano and chatted to Sprocket? He's such a...such a dog. You know? Stuff doesn't really bother him that much.
Now, sure, it will have taken him a while to get over Jim's death, but I don't think it will have left him depressed. He may have just moved out of the lime light, thinking that wasn't the place for him anymore. Like, maybe he would have 'retired' much as Frank Oz did. But I don't imagine for a minute that he wasn't down at his local pub, playing the piano and cracking out old dog-jokes with a talking Beethoven. And I don't think that Jim (in fanfic world) would have wanted him to become depressed or to spend every day missing him either.
When I wrote the Dark Universe series, set in the world where Kermit was never born, Rowlf and Clifford were the only characters that I honestly did not feel would have been that affected with or without Kermits influence in their life.
Anyway, that's really my thoughts on the subject as inquired about by Aaron, and no reflection on the story-telling of Miss Kermie.
Miss K, the idea of Rowlf curling up in the place of Jim's Coffin (much as a dog with a lost owner) is totally something that I can see him doing! But I'd like to believe he'll be able to move on from that place before too long. *hugs for Rowlf*