Though the plant itself is generally very hardy, some plant parents find it very hard to care for, usually with the most common issue, overwatering. It is absolutely vital that String of Hearts is treated as a succulent. They need their soil to dry out between watering as they store water in their tubers in the soil, or grow on their strings. It is also important for the plant to have some sun during the day, preferably morning sun, and to use a well-draining soil. Over winter you should cut back on water and let the plant rest as they enter their dormant period.
Problems
Yellowing and dropping leaves - overwatering. If the roots have rotted there is unfortunately not much that will save it. Try to repot the plant gently in a mix of well-draining soil, mixed with sand or perlite.
Neglect in watering is KEY with Ceropegia Woodii. Try underwatering rather than being generous.
Wrinkled or curling leaves - too cold