I wish this was a bit better explained. I let them sleep for most of the day, thinking they were on a cooldown. When I tabbed back in, they were still asleep. I personally don't think this is a great mechanic in it's current state, as it could very easily lead to someone softlocking themselves by being too poor to afford it. Imagine having all Furrymon asleep, spending the money carelessly on upgrades, then realising you're softlocked because you don't have enough to wake them. Almost happened to me.