Grass seed, when properly stored, can keep for years, but its viability and germination rate will slowly decrease over time. A good guidance rule is to try and use up all the grass seed in a certain batch within a year after its test date. Also, keep in mind that no matter how carefully you store your grass seed, if it was damaged before storage--for example, if it was not sufficiently dried, or invested with fungi--no amount of careful storage will preserve it.
Ensure that your grass seeds are dry. If not, spread them on fine mesh screens to dry thoroughly before storing, or else discard them.
Seal the seeds into a dry, airtight container; a bucket with a tight-fitting lid works well, as does a small jar or kitchen canister, depending on how much seed you have to store.
Make a note of the test date from the original seed container and record it on the airtight container.
Store the seeds in a cool, dark, dry place. The refrigerator is perfect for this, if you have room for it--otherwise, a well-ventilated shed or the garage may be your next best choice. Make sure not to freeze the seeds; the temperature should ideally be below 60 degrees Fahrenheit but above freezing.
Keep your storage place as clean as possible, clearing out all debris, rotted seed, and anything else that might attract possible insect or fungus infestation.