I think good friendships can be sustained if you avoid making the murderer of their father figure your new best friend.
Seriously, doing that means you don't give a fling about Alistair on a personal level, so why would a Loghainbro Warden even care?
Caring about someone on a personal level =/= always agreeing with them, or acquiescing to their wills. Nor does sparing Loghain mean the Warden's his best bud, or even that the Warden agrees with or supports Loghain in any way.
Of course, hanging around with your friend's father figure's murderer at all is probably going to end your friendship, but it still doesn't necessarily mean you don't personally care for them. Unless your view of "personal care" means "care beyond all else", which would make having more than one friend really hard.
Anyway, if Alistair is king and both Loghain and Alistair are alive, he'll utter "Sadly, Loghain still lives" to Aveline in the second game. So, he's not over that. I imagine it's possible to restore some of the friendship, to a grudging degree (you
did make him king), but there'll always be a heavy shadow over it, even if there are moments where they seem like ol' buds again.
Worth noting,
Awakening Alistair's dialogue is exactly the same no matter if Loghain was spared or not. They didn't really account for Alistair's feeling beyond "king", which is a flaw in the writing admittedly.