On online forums carers, and not just carers for people with dementia, complain about their life 'being on hold'. It's pretty obvious really - life is never on hold. The sun rises and sets, you get a day older, your life goes on. What people are really saying, I guess, is that they are unable to live the life they would wish because of the circumstances they find themselves in. But this is a feeling that many, many people have, not just carers. You could say that it's part of the human condition, one of the things that makes us human even - it's not a problem your cat has.
It's more understandable maybe in carers than in whinging teens or workaholic thirty somethings who, in all likelihood, still have much of their life ahead of them (though we mustn't forget that people of all ages can have caring thrust upon them).
There's no solution of course - you're bound to feel like this at times. But if you try to carry on finding life interesting, even the difficulties that you're facing and possible ways of lessening them, and to get satisfaction from something that in more normal circumstances might pass unnoticed, like seeing the person you are caring for laugh (if they can) or actually completing a task on your mental 'to do' list.
And then of course there's music, friends, family, reading, memories..........
And that life that you could have been leading might not have turned out too well anyway.