Short answer is no. Subscription rewards are only given out when you log into the game, and have no timer on them (other than expiry date of mail sent).
This means that if you are unable to play the game or miss playing for the day, the subscription will continue from the next rewards listed. The game will progress the subscription, as if no time was lost. The game will not stack days from the same subscription up and then send them all at once.
E.g: If I collect the rewards from Day 9 of my subscription but can't play for a few ways, when I log into the game, I will receive the rewards from Day 10 of my subscription, but I don't receive Day 11.