How should pomegranates be stored?
According to this page:

Whole fruits can be stored for a month in a cool, dry area, or refrigerated up to two months. The seed pips can be frozen in an airtight bag up to one year. Fresh juice should be refrigerated and used within two to three days.

In my experience in a very dry climate (Colorado) after a couple weeks the skins become desiccated and very hard—you need to saw through them with a serrated knife—but the seeds are still mostly unaffected. They will shrink somewhat, but still remain unspoiled and flavorful.
However, if you refrigerate them, ensure that you do not let them get too cold. According to this page:

[…] exposure to temperatures below 5°C (41°F) during storage and transport for longer than 4 weeks is a major cause of deterioration […]
The minimum safe storage temperature is 5°C (41°F) for up to 8 weeks, if decay is not a problem. For longer storage, the temperature should be at 7°C (45°F) to avoid chilling injury, but decay […] and weight loss may become a limitation.


Sorry that the photo is not better quality.