Yes people do tend to fart more often as they get older and it has to do with changes in the body as you get older and reach old age.
As people begin getting older and reach old age they produce less enzymes that are needed for digestion which means that it's harder for older people to properly digest foods which then causes more gas build up in the stomach.
When the person can't break down those foods properly then the gas builds up and then they fart more often the older they get.