What's the temperature in your house? I'd been getting very thin SCOBYs, too, and recently got mold for the first time since starting KT 2 years ago.
I did a little research and found that KT ideally needs 70F or above and never below 60F. Our thermostat was set to 64 during the day and 57 at night until Justice was born.
I am getting a fresh SCOBY and am going to keep my brewing jars either on or next to a heating pad in winter from now on.
I didn't have this problem last winter.