Same here Mary! I could never take the stress of having a $100 daylily! I'd have to sleep in the garden with it to make sure it survived! I'm too cheap for those anyway!
In the little experience I've had, some daylilies increase different than others. Some seem to grow a new plant that isn't attached to the original, but the roots seem to be tangled together. Others seem to grow off of the side of the original, and they are stuck together at the crown. I sure do prefer to divide the ones that aren't stuck together, and I panic a bit when cutting apart the others. Haven't lost one yet due to being careless when doing this, but it always worries me. Therefore, I only divide if I have to do it.