I no longer have Premium Membership, however I purchased Pet Slots with NC. Why do I have to abandon my pet?

When your Premium Membership expires, you are prompted to select a pet as "idle" as these pets are under your Premium Membership slots.
 
Once you have placed your pet in "idle", you can retrieve your pets and they will automatically be placed in your NC purchased slots.
 
If you have enough empty slots, please visit your Pet page, scroll through and click your idle pet. There should be an option stating "Bring home __(your pet's name)__?"