While there is always the possibility that more than one thing is slightly off for a plant, the primary concern here is likely to be your soil conditions. The roots and rhizomes of the easy going ZZ plant (Zamioculcas zamiifolia) are its weakest point and soil that stays slightly too damp will gradually rot rhizomes and cause the plant to deteriorate. This is particularly apt to initiate in winter when the plant is not in active growth and should have extended dry conditions. But a pot that does not drain well, soil that is too moisture retentive, water allowed to remain in a run off dish, repotting in a container that is too large, or a container type that stores the run off water in a contained space or tight fitting dish, also create this problem.

Your plant should be kept in a container with a drain hole that allows water to flow freely from the pot, not into a contained space or tight fitting run off dish. Going forward,  bring the plant in its pot to the sink when you water it. Water the plant moderately with tepid water in the morning, making the potting mixture moist and allow it to drain in the sink for 15 minutes before you return it to its position.

During the growing season, allow the soil to dry completely at the center of the pot between waterings. Some people are good at assessing dryness with their finger and other people prefer to use a moisture probe. If in doubt, wait to water the plant which stores resources in its rhizome that allow it to wait out dry conditions. In winter, the plant enters a period of slow growth and should receive reduced water, approximately once a month.

If you re-potted this plant, check that you have it in a fast-draining soil which will simulate its native habitat. A succulent soil works well. 

Other care conditions to check and adjust if necessary:

• Keep the plant just out of reach of direct sunlight, even if it is positioned in gentle light, like an east-facing window where it should be several feet away from the window.
• Avoid placing the plant near a heat or air conditioning vent. The strong blasts of air stress and confuse the plant which comes from a tropical habitat with steady temperatures. Keep it in warm home temperatures, between 70º and 85º F.
• Do not over-fertilize. Feeding twice during the growing season is enough.
• In winter, the plant enters a period of slow growth and should receive reduced water, approximately once a month.

It is hard to know whether the roots and rhizome have been damaged already but if you correct any points of care you see here that need adjustment, you should see reduced dieback if the roots and storage system are in good shape and healthy new growth in spring and summer.

Courtesy of NYBG Plant Information Service