binkies from Ivy's Hut are guranteed drops. so far I've received a Binky on each collection. it takes 2 Binkies to make Chapter 1, therefore we can make one Chapter 1 per day.
maybe you should post in the Bugs and Issues thread if your problem continues as it's not possible to finish the event within the time given with only 1 Binky drop per day.
try all the normal procedures on your device to see if the problem corrects itself, especially checking if you're using the latest CS version and also not playing with 2 devices with different CS versions.
good luck!