Cut-up raw onions keep satisfactorily in the refrigerator for up to a week when stored in an air-tight container. However, you should never store whole raw onions in the refrigerator.
The refrigerator is too damp for uncut onions. Dampness coupled with the appliance's poor air circulation causes onions to spoil. The best storage area for onions is a place that is cool, dark and dry with good air flow. Keep onions in a mesh bag to ensure ventilation. Because scallions and chives have a higher moisture content than onions, storing them in the refrigerator is fine.
In addition, do not store onions and potatoes near one another. Spuds emit moisture and gas than accelerate onions' spoilage.