First don't store photographic solutions in a refrigerator. Certain components can come out of solution due to the cold and be very difficult to bring back into solution. The only developer I know of where the manufacturer actually recommended such storage is Ethol TEC.
The lifespan of a developer depends on the nature of the developer and varies widely. Rodinal and HC-110 concentrates last for years. Most developers are good for about 6 months if properly stored. Best to make up an amount that can be used in a reasonable length of time depending on your own usage.