Since I know what sencha you have, I can say this. Both genmaicha and flavored sencha should remain "fresh tasting" for at least a few months. I say fresh tasting because often the flavoring and the toasted rice will remain fresh tasting longer than the actual tea leaves will.
Japanese tea leaves, once open begin to lose flavor immediately and would lose a noticable and significant amount of flavor within 2 months. I like to use any fresh Japanese tea within 6 weeks or so of opening.
I store unopened tea in the fridge, adding at least a bag layer or 2 (preferably foil zip lock type if you have any from tea you purchased previously) and keeping it as close to 33* F as possible. When you take it out of cold storage, let it sit several hours until it is room temp. This will prevent room humidity from condensing on chilled leaf. Unopened tea stored this way will last much longer than at room temp.