I've not seen a cat's life through to the end before, so this is a new decision for me.
The lovely cat who has been with me for fourteen years has recently had episodes of being totally listless for a day, falling over when she walks, tumbling off furniture with no effort to save herself, not eating or drinking. Then the next day, she's back to her usual self, bright-eyed and alert, apparently right as rain (although a bit hesitant and weak on her legs), wolfing down any food we give her, and most indignant when we won't let her out on her own. This has happened twice in the last couple of weeks.
Having examined her, the vet's not sure what's causing this, has run many tests, eliminated many possibilities, and has suggested neurological diagnosis. To the disagreement of others in the house, I'm really reluctant to do this. Firstly, the cost: it's highly specialised and would be phenomenally expensive for the diagnosis alone, much more than insurance would pay for (we contacted them and checked), and it might not cure anything. It's also likely she's near the end of her life anyway; she was a stray fourteen years ago, and wasn't a kitten then. To me it feels that at her age, there's only so much that could be done for her, and it would be wrong to put such an elderly cat through complicated treatment which would involve lots of travelling (which she doesn't like), only to find out in a very expensive way that it's an illness that cannot be cured. My own thinking is that she's had a long and happy life, and it would be kindest to leave her as she is while watching her closely, mostly keeping her indoors, and to consider putting her to sleep if the bad episodes become more frequent, or she is like that all the time.
If it comes to putting her to sleep, it would be very sad, but I would not have a problem with that if it's the right thing to do for her, and if she might be close to dying anyway.