Why flaxseed sealed in containers once opened needs to be refrigerated and yet has to be consumed within 4 days?
Here is a quote from a "Mens Fitness" article on flax seeds:  


  To get the nutritional and health benefits of flax seeds, aim for 1 to 2 tablespoons of flax daily. You can purchase flax seeds whole or ground. The ground flax seeds may be easier for some folks to digest over the whole variety. Store flax seeds in a sealed plastic container in a cool, dark place for up to 4 months. To maintain freshness longer, you can also store flax seeds in a sealed plastic container in the refrigerator or freezer.


That quote of 4 months for whole seed I think for un-ground seeds 4 months without loss of quality in sealed container should be safe and a fairly standard claim.  They need that for shelf life for selling.  4 days after grinding might well be as they will start to lose quality due to loss of essential oils.  But unless they have done something unusual I see no reason the whole seeds cannot be stored longer.  If the particular source has done something like stored them long term in an inert environment requiring the entire bag be used immediately on opening, I would look for a new source myself.