If you do not feed your sheep long enough, do not brush them, or leave them out in the rain, they will get sick (shown by a purple particle effect) and no longer produce wool. You need to give them Animal Medicine to cure them.
Sheep give larger, more valuable wool the more they like you. You can improve the relationship by petting them once per day, letting them out when it is sunny, keeping them inside when it is raining or snowing, and feeding them fodder by hand (instead of using a trough).
It is important to note that relationships are per person. If playing in multiplayer, if you want large wool when you shear the sheep, you will have to personally raise your relationships.
Multiple Products Edit
Sheep will produce up to 5 wool at a time if you feed them treats. It takes 29 Sheep Treats + 2 generic Treats per level up to a total of 5 products.