Sending a single guy to the moon - what if something goes wrong and he needs backup? Oh, wait...
When I first saw Moon, the fact that the base was on the far side of Luna struck me as a fairly inane decision. Most of the material that they're supposedly mining from the surface would have ended up on the near side; the choice to put the protagonist on the far side, out of reach of direct communication, seems like a lame excuse for a plot point — he needs a reason to have a communications satellite before it can break down and isolate him. And then I realized there were probably political and economic considerations — people had probably complained about the mining operation potentially "disfiguring" the side of the moon we're familiar with.
Wordof God has confirmed this. There were ecological considerations as well — they didn't want to screw up Earth's wildlife by changing the reflectivity of the visible lunar surface, through installing solar panels for the base or whatever.
I initially assumed that the clones died after 3 years due to a defect in the cloning process. My mother-in-law (clever lady) pointed out that each of the clones suffered from radiation sickness. It seems to me that the lunar base lacked adequate radiation shielding, probably as a cost-cutting measure for the corporation. It's terrible to think about, because if the company had not skimped on the base design, they could just send up a real volunteer for one human lifetime. Instead they planned to create an undefined number of clones and slowly watch as each one suffers fatal radiation poisoning. The corporate way involves the death of 20x more sentient people.
As Chernobyl showed: robots are much more vulnerable to radiation than humans; the robots the Soviets sent in were fried within a few hours. It appears the base has adequate shielding from cosmic radiation otherwise GERTY wouldn't function, but it appears Sam's regular excursions onto the lunar surface raise his exposure above the threshold. HarfynnTeuport
It's cheaper to radiation proof a single robot than it is a whole base.
The original Sam is implied to have made it back to Earth, though — at least, 15-year-old Eve calls for her Dad at the end of the video call. Since the whole point of the scheme was (apparently) to save money, it's likely the clones were designed to only last three years because that's how long they need to last... The original Sam had to actually agree to go up there for three years, and actually come back; each subsequent clone had to believe the same thing, since the whole point of the cost-saving was that they could inherit the original Sam's memories.
Original Sam only needed to be up there for a couple of weeks as the clones memories start at the beginning of Sam's contract, this means that Sam and his Wife must have been in on it though, as she would have had to record those messages.
It's possible that Original Sam got radiation sickness too, but held on for long enough that he got cured back to life on Earth. Most Sams appeared not as sick as Sam 1 finally was (his condition may have been worsened by crash), when they lowered themselves to "sleep".
Lunarcrete (which the base is supposedly made of) is also easily able to block the level of radiation found on the Moon without additional expensive stuff, one of the reasons it's been researched.
I've read an interesting concept in Wildgoosery's fanfic, it states that the clones have a lifespan of 3 years so that they would decay and die naturally to avoid internal conflicts in GERTY's programming.
I regarded it as a bit of a plot hole that one of the Sams could get home using the H3 shipping container, as it had an unrealistic resistance to G-forces and was inexplicably filled with air. However, I thought a little more about the shipping containers, and figured out how it would work, and most likely did: Containers are probably recovered on Earth, emptied of their contents, then filled with supplies such as food and medicine and sent back to the base. It would make sense that they'd build it to be an air-filled, less damaging environment, so that they would have a better chance of being able to send up something unexpected that they would inevitably need. It's a mildly contrived explanation, but if you need something to solidly put your mind to rest about it so that you can enjoy a fantastic movie, it works great.
At one point, Sam, with a marker, draws a series of smiley faces on one of the stainless steel walls in his bathroom facilities. The way the wall is lit, you can see the smiley faces before he draws them in, like the surface is smooth where the drawing would be. This isn't an error—since the base is reset after every "shift", the smiley faces are erased, and the next Sam draws them on. It's been done so many times it's damaged the wall.
There's a post-it note on Gerty's front with something along the lines of 'service rover 3 boom' written on it. How come Sam never noticed it was written in what is presumably his own handwriting?
He thinks he's just woken up from a crash with minor brain damage, having forgotten the previous couple days.