Agreed with the above. I know it's hard letting go - I lost my childhood pet, who had been with me since I was young, had experienced all of the hardship our family went through with us. She was taken from me and I was bitter and angry; I felt she had so much left to give. She wasn't supposed to go that young.
And 15 years old doesn't seem very long to us humans either. But, for them, it certainly can be a long time. Some animals just age faster than others, especially when they get sick.
I don't blame your wife for wanting to hold onto her. I feel the very same way - nobody ever wants to say goodbye to someone they love. It's selfish of us, but a natural feeling nevertheless. No shame in it.
That said, if your cat's quality of life is slowly going down the drain, the best option would be to let her go. The less she has to suffer the better. Instead of waiting for her to wither away, why not let her go on your terms? Maybe the vet (or another vet even) can come and do a home visit? That way you can take the time to prepare, say your goodbyes, and know that she didn't have to die a slow, possibly painful death.
It's horrible because in this case, both options suck. But no person or animal deserves to just wither away. They should be able to pass in peace, with their loved ones by their side. And in this case, you and your wife have the chance to do that for her.
Proud parent of Scamper (age 12) and Robin (age 4)
At the rainbow bridge: Slippy, Faramir, Gabriel, Lucky, Ammy