Maybe he does have some sort of feelings for her that he just feels he can't recognize yet.
I would gently disagree with you. I'm certain he does recognize it -- he's old, I just can't consider anyone who's survived as long as he to be that oblivious. He purposely separates himself from her when he's able -- such as in in Cry Wolf, at Doc's funeral. He sat in the pew behind Bran, his alpha, rather then with her. Later on Anna recalled seeing her at the funeral. So Sage was there, but not so close. I believe Patty would have specifically pointed out if Sage had been sitting near Asil. Rather then when Anna randomly recalled seeing her once Sage came to Charles's home later. Asil probably felt that in a church with the Marrok present -- no one would have threatened Sage. He likely felt she was safe enough. Besides, he was more facinated with tormenting Charles who he knew would sit with his father/alpha. It's a matter of priorties -- torment the alpha's pup and trigger a fight with the alpha or Charles or protect a woman who isn't his in a location where she's fairly protected.
I live in a relatively small town. Everyone knows your business -- good and bad. Aspen Creek is even smaller so I can only imagine the gossip it would invite. He's a private man, I think getting into his business would certainly be a death sentance. He's already borderline suicidal (that early in the book, anyway). Anyone that old would have a strong sense of honor -- it would have been rude to hurt a woman that way -- being born in the 800s is a far cry from 2010.
I think he allows her around because: a) he's dominant and has the need to protect those who are less dominant and needs protection (she's been injured in the past), b) no threat to his position in the pack, and c) doesn't take offense to his moodiness (because it's not directed at her).
Of course he likes her, she's nice to him and of course, beautiful. But I think for now he's willing to keep her as arms length -- as a puppy in need of protection from others, but he keeps her close enough to pull in at a moment's notice if someone should threaten her.
It's hard to see from this point forward, not much was said about Asil in the last book, Hunting Ground. And Sage wasn't mentioned at all. I think Anna would have mentioned something more if something had changed about their situation. He's still trying to recover from the last 200 years. I think any relationship for him is a ways off. He likes her too much, to be that cruel to her - it's a matter of curtsey.