Thank you for playing! I’m glad to hear that you had fun with the game. :)
The number of furballs in your possession is indeed limited, and it is shown in the interface. It may not be obvious, but when you send a furball to a task, it then instantly returns to the tower. But if it rolls away from the map, it is lost forever. So, you need to manage and keep them busy. New furballs can be acquired by clicking on the tower. The price is 5 gold coins. This is said on the game’s page but is not apparent from the game itself.