Mechanically, automatic feeders should last as long as the batteries last. I've seen automatic feeders that are well built that last for 10, 15 years. It's more, can the fish survive just being fed via an automatic feeder. You have to have the feeder always working. I find when people rely on automatic feeders, they get very lazy and it just causes people to neglect their aquariums. Part of what keeps people interested in the aquariums is the daily interaction, which is mainly the feeding of their fish. When you put food in the tank and the fish eat it, it's enhancing the bond that you have. So for that reason alone, I don't recommend automatic fish feeders.
However, if you're very busy and you want to put an automatic feeder on the tank, don't forget about it. It's going to run out of food after about two or three weeks and you're going to need to restock it. Even forgetting for a week is going to be a problem because those fish really rely on the feeders.
Another problem with automatic feeders is they drop the water. Most foods float, so when they drop the water on the surface of the tank, it has a tendency to deliver the food into the overflow box where it goes right into the filter, bypassing the tank itself and not really benefiting the fish. So make sure that the types of food that you use doesn't get sucked into the filter. You want to use a sinking pellet. And try to vary the diet. Take two or three different types of food, mix them in a container, then put those into the automatic feeder.
But I only like to use feeders when in a bind or when going on vacation. You really want to feed your fish every day, manually. It's also a good way to spot problems, see if the fish are not eating or if they are eating. So for all those reasons, I'm kind of against automatic feeders.