There's no expiration date on the crystals themselves. Or, at least...there's no way to see any date on them because it's not an inventory item, just a counter, and that would be an extremely dickish move to have things expire without any way to see when that's going to happen.

But there is an expiration date on what you can trade them for. This is because there's a limit on how many of each item you can purchase, and occasionally this limit would have to be reset with the store getting restocked.