Anniversary Gifts

So in EUW, each day of the anniversary gifts doesn't come online until the evening. As some who at times can only play in the morning before work, does this mean i'm going to miss out on rewards because i can't play a game during the 'american' next day, despite having played again on the same calendar day but before the mission is available? If so, how long do the missions stay online? If i miss a day or two because of this does it mean i can no longer get the gifts?
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