Diagnosis
The silicone release pad inside the curling chamber is worn out or has hair/oil buildup. It's lost its non-stick surface.
How to Fix It
Unplug and let the unit cool completely. Use tweezers to remove any visible trapped hair. Dampen a cotton swab with 99% isopropyl alcohol. Scrub the gray silicone pad inside the chamber thoroughly. Also scrub the surface of the spinning barrel. Let it dry for 10 minutes. The pad should feel slightly tacky, not slick or gummy.
If That Didn't Work
The silicone pad is permanently degraded. Conair sells a replacement chamber unit. Search for "InfinitiPRO Curl Secret chamber replacement." It clips in. No tools required.
Heads Up
Never use oils, conditioners, or silicone sprays on the pad. It will dissolve the material and make sticking worse. Clean with alcohol only.