Many pets are only active for 90 days, although sometimes permanent pets are available in the Cash Shop.
After 90 days, your pet turns back into a doll, and it needs to be revived before you can play with it again. To revive your pet, purchase a Premium Water of Life from the Pets → Pet Skills category of the Cash Shop. The item costs 2,400 NX.
You may also be able to find it in the Maple Rewards Shop (available via the Event → Maple Rewards Shop category of the Cash Shop). The item is 2,400 Reward Points. Double-click to move the item from your Cash inventory to your character's inventory. Then double-click the item to revive your pet.
If you have more than one pet, you can select which one you want to revive. Reviving your pet will give it another 90 days of life.
On non-Reboot servers, Wisp's Wondrous Wonderberry sold in the Cash Shop may provide a Concentrated Premium Water of Life, which revives pets for 270 days!