If you have a Furby (Tiger Electronics/Hasbro) toy that is constantly sleeping (meaning it wakes and goes straight back to sleep), there is a simple fix that works for the majority of Furbies with this issue.
Unfortunately this is a common occurrence with this toy, which were made from 1998 through 2000, so even the best condition ones are getting on in years. This is an issue of general wear and tear, and isn't always linked to rough play/bad handling.
1. Wake your Furby and let it go back to sleep.
2. While the Furby is asleep, press and hold down it's tongue.
3. Still holding the tongue down, turn the Furby upside down.
4. Still holding the tongue, give it a gentle shake around.
5. Still holding the tongue, turn it the right way up.
6. Wake the Furby as normal, and the issue should be resolved.
7. Repeat as necessary.
Note: I have not tested this method on Furby Babies, but the principle should be the same.