How can one compensate for fasting months or days missed during captivity, with strenuous labor and being prevented from praying and fasting, especially given that current fasting poses difficulty due to deteriorating health?

If prayers are missed, they must be made up for, by their known number, or by what is most likely, until one's duty is discharged. As for fasting, if it does not affect one's health, all missed fasts must be made up before the next Ramadan (definition). If one delays making up the fasts without a valid excuse until the next Ramadan begins, then one must make them up along with an expiation of feeding a poor person for each day. The expiation may multiply with the number of years. However, if the delay was due to an excuse, there is no expiation. It is recommended to hasten making up the fasts and to do so consecutively. If fasting affects one's health by worsening an illness or delaying recovery, then breaking the fast is permissible, followed by making it up after recovery. There is no sin or expiation, even if Ramadans follow consecutively. One only resorts to feeding (as expiation) if one is chronically ill with no hope of recovery, or is an elderly person unable to fast.