Someone missed a few days of fasting during Ramadan because of a temporary illness. He should make up these fasts when he is not ill anymore. However, is there a time limit to when he can make it up. Can he make up it anytime he wants like after the next year's Ramadan or is this a sin for delaying making up fasts for no excuse.? What if he was an adolescent who has started puberty but fasting was obligatory for him and he missed some salah due to illness and he wants to make up for the ones he missed but fasting is still hard for him and the next Ramadan is coming and he still has not made up for these fasts? Can he make up for these fasts after the next Ramadan or will he be sinning?
There is no guarantee that one would still be alive that long in the future. One should make up debts and duties as soon as possible.
The imams are agreed that whoever does not fast some days of Ramadaan has to make up those days before the next Ramadaan comes.
More details in this fatwa.