I'm happy to say that I was attracted to this song right off and had it on repeat during the first few days that I owned it!
Many people panned it, but I found it to be an oasis between Crumbs and Original. It has the kind of subtlety that "When I look at the world" has. It doesn't blow you away, but it's good. And unlike "WILATW" it doesn't have to try to wake up the back side of the album, like WILATW was supposed to. (IMO ATYCLB's biggest problem is that the 2nd half just isn't very rousing) And since it doesn't have to rescue the back side of the album it's free to be what it is. If Yahweh didn't exist, this would be the coda like Mother's of the Disappeared, MLK, Grace or the Wake Up Dead Man.
To answer the original question...
(I get sidetracked too easily)
I agree that it's from his Dad's perspective, and the Old Rose is all the hurts that we hold onto throughout life. It could be that he lost his wife at a relatively young age and can't see what it's all for. Or it could be that his boys didn't love him well enough, or it could be other unimaginable slights and disappointments. Bono reminds him (or himself) that hurt is still preferable to being numb, or being dead.
It's a common theme through the album and a theme that I think is important to remember when things are going sour. It can't always be wonderful, and yet there is purpose in the pain. Without the pain, we wouldn't know pleasure. We wouldn't appreciate it when things are good.