I am so sorry to read that your basenji is not well and perhaps nearing the end of his life. I've known so many pet owners who, after their pet passed away, said "I waited too long." I had three basenjis; they were all 15-17 years old when they went to the rainbow bridge. I almost didn't get any more dogs after they died because those decisions were so difficult. I think that using eating as the marker is not enough. What I think about first is DIGNITY. Human beings who are nearing the end can think about dignity but our pets can't. I think it is up to us to let our pets go before they are peeing and pooping everywhere or acting confused. Surely something must tell them that this is not their normal behavior.
I have a wonderful article written by Dr.Marc Bekoff, an animal behaviorist, who wrote about how difficult it was to make the decision. Unfortunately I don't have a link; I just have the article. He talks about having to make the decision about his 12-year-old dog. Please forgive me for including so much of what he said in this response, but I couldn't have said it any better, and each time I have had to say goodbye to one of my pets I have turned to this article for comfort and understanding and knowing that I am doing the right thing . I recently had to say goodbye to my 16-year-old cat and it wasn't any easier than the last time but Dr. Bekoff's words comforted me:
Jethro knew I’d do what’s best for him and I came to feel that often he’d look at me and say, “It’s OK. Please take me out of my misery and lessen your burden. Let me have a dignified ending to what was a great life. Neither of us feels better letting me go on like this.” And I feel he told me that the moral dilemma I faced was no predicament at all; that I had done all I could and that his trust in me was not compromised one bit — but, perhaps, strengthened; that I had made the right choice; that I could go on with no remorse or apologies.....Our companions are counting on us to be for them in all situations, to let them go and not to let their lives deteriorate into undignified humiliation while we ponder our own needs in lieu of theirs. We are obliged to do so. We can do no less.
Your basenji will thank you, and you will be at peace, knowing that you made the right decision.