I have a dying azalea bush in my yard. It only has a few leaves on the end of each of its branches; mostly it's just a stick in the ground. Each season I think for certain it has died over the winter, but each spring it surprises me by sprouting a few tiny new leaves. Showing just enough green so that I know it's still alive, struggling, trying. I almost wish it would just die, so that I can plant something heartier and prettier there, but I can't bring myself to pull it up while it's still got green buds. Even if it's just barely holding on.
It's fighting to live, and I respect that, so I leave it there.