Our older cat only started to want to sleep with me when she was two years old. There's a specific placement I have to abide by (on my left side with a little pillow holding the covers up, and she snuggles into me, and I have to keep my arm over her). One wrong move and she's GONE. All my cats have slept with me as they get older. Kittens, no. Although our 4 1/2 month old kitty sleeps in the guest room and will snuggle with whoever visits us. They make up their own minds, you can only invite them...