What is the age limit on promotions in the U.S. Army Reserves?

No but what they might be saying is that currently you can not serve past fifty-nine and ahalf. If he does not have enough time in grade when he reaches that point he also will be discharged from the active reserves then he can not be promoted. They have talked about upping the age that a person can stay to 62 but that has not happened as of yet. The time left on his enlistment goes over to inactive reserve status when this all happens and they may have let him re-enlist for a point beyond 59 just in case this does change. Years ago when a person retired they used to promote them to the next higher rank but that stopped in 1979 and also you now have to serve a minimum of two years at that rank to garner the higher retirement pay that goes with it if it is a top three enlisted or senior officer rank.

Is he an Officer or Senior NCO? How long has he been in the Reserves, time on Active Duty?.

Promotions for senior members for the military are centralized at the DA, ARNG, or USAR HQS.

They are looking at the "whole" picture.

The qualifications of individuals, not age!

The age limit is put in place to factor in the cost of training vs the remaining useful lifespan as a soldier. No matter how fit, it's just not economical to take older individuals.

SO LONG AS ONE CONTINUES SERVING IN THE ARMY IF HE QUALIFIES HE WILL CERTAINLY GETS HIS NEXT RANK. Normally when one goes to Army Reserves one should be happy if he is taken up but he will not be given any promotion as I know which is common mostly in all countries,

IN FACT IN SOME COUNTRIES though he is taken in reserves his pay given will be as what he was getting in his previous rank .THIS CAN BE CHECKED

yeah, the issue is you have to be able to serve X number of years in the higher grade before you ETS or mandatory retire, so if he's up against it then they won't bump him up. You can search for the exact regs.