Matcha is very delicate stuff. It doesn’t like heat, it doesn't like air, and it doesn’t like light. Once it is ground, the clock on its shelf life — about a year, possibly longer, under ideal conditions — starts ticking.
And that’s for unopened matcha green tea; once it’s opened, it really should be used up reasonably quickly, say within a few months, for optimum freshness, color, and taste. It will still be fine after that, especially if it's been refrigerated, but there's really no reason to “save it for a special occasion” — it's never going to get better, so it’s vastly preferable to enjoy it in its optimum state. Stale, dead matcha is no fun — drink it when it’s hypergreen and vibrant.
Matcha should either be stored in the freezer, if you plan on not opening it for a while, or in the fridge, once it’s opened. In both cases, matcha is happiest and remains maximally vibrant the longest in UV-proof black-violet glass best. But whatever you're using, be sure it's as air-tight and light-tight as possible. Our glass (made in Germany) is ideal. Always minimize the amount of light and air that comes into contact with your matcha -- close the cap when you're done making your matcha, and put it back in the fridge, pronto.
NOT storing your matcha properly won't make it go rancid or anything like that (there's no fat in it to rancify), but it will make it lose its its vibrancy, color, and taste.
Keep it in a good container, and keep it cold! It's absolutely key to fostering the tea’s taste, color, umami content, frothability, and health properties.