I hate to say it, but there comes a time when you have to say goodbye. Hanging on for your own sake is not the right thing to do. The dog's quality of life and letting it go with dignity and without suffering are paramount - and far more important than the possible distress of the owner.
In my experience, a Basenji will tell you when it is time to show him/her that last kindness, that last act of love and send them on their way. You get one last chance to show them how much they mean to you and that is by letting them go.
In all my years with Basenjis, I have never once had one die naturally. They come and tell me their time has come and I fetch a spade and call the Vet. He always comes to the house - there is no way I'd send a beloved friend on that last lonely journey from the Vet's office - and we sit in the sun with the dog on my lap. Up to now, Marvin's hand has always been on the head of the dog, but these remaining two, now almost 13 and 10, will have to make do with me on my own.
They are all buried at the bottom of the garden with headstone laid flat to accommodate the lawn-mower.