There are older missionaries, and they come in 2 varieties: married couples and single sisters (either spinster or widowed.) The only special requirement that they have is that they be retired.
Most senior missionaries don't do the door to door stuff that us youngsters do, instead they'll fill special roles, like Church Educational System (CES) workers, military relations (we have a couple doing that in my branch right now), mission support (which usually means manning the office), health services, welfare services, and mission presidencies, among many other roles. While I'm not sure what exactly goes into what kind of a mission you get, I do know that the couple's skills are a heavy factor in the decision.
They serve for 18 months, and many don't go on just 1 mission. I've known a few who go on a mission, return home, then go right back out on a new one.