This could be a classic problem of low air flow as rduhon suggests.
I am no expert at A/C, but I did install a unit in my last boat as a DIY project. And, of course, it did not work, and I had to figure out how to fix the problem.
The issue was that I did not install sufficient duct work from the A/C unit, which resulted in insufficient airflow across the coils, evaporator, or whatever its called. In a sense, I suppose airflow "draws" cold air away from the coils so that they do not freeze, and this cold air is what cools the boat.
A coil is like a radiator, and if it freezes, damp air condenses on all of the fins of the coil and restricts air flow, which results in more restriction, which results in more freezing. At some point, you'll have a block of ice.
A clogged air filter can also cause this, or even having the sofa too close to the air return vent, basically anything that restricts air flow - incoming or outgoing.
It does seem odd that this process even works, as during normal operation, you are not too far from freeze up anyway, and some condensation occurs on the coils regardless, but not to the point that it begins to freeze. This is where the condensation that must be removed from the air conditioner comes from, and I suppose it also lowers humidity.
After talking to a couple of Air Conditioner experts at a local boat show, after describing my problem, they immediately figured out that my duct work was not sufficient. They also indicated that many air conditioner units are not properly designed by the boat manufacturers, as many of the plenums are either too small, or have hard transitions (i.e. too many right angles), or use what is best described as dryer-duct flexible hose that causes air flow restriction.
On my current boat, I have found that my forward A/C unit supplies both the front berth and head, and if the air duct in the head is shut off, the unit will freeze up. This then is one of those marginal installations the A/C guys described.
So I keep the duct open in the head to maintain airflow. This results in the head being like a meat-locker, but its better than the Air Conditioner freezing up.
How to tell if the Air Conditioner is freezing up?
The classic symptom is that when you first start the Air Unit, you get pretty good air flow, but over time, no air comes out of the unit. If you turn the unit off for a half-hour, then you again get good air flow, but after awhile, it freezes up again, and no air comes out.
If you were to check the coils on the air unit, I'd bet you would have a frozen block of ice across the fins.
I suppose this could also be a situation with low freon, I don't know. As I stated, I am no expert. But in my last boat, the air unit was new, so the freeze up was definitely from lack of sufficient airflow.
One other issue I can think of is that 70 deg may be too low of a setting. Try 75 through 78 deg. Remember that the air conditioner is also removing humidity, and 78 deg is usually pretty comfortable. It could be possible that 70 deg is allowing the air unit to run too long, and after lowering the air enough, that the return air becomes cold enough to freeze up on the unit.
I dunno, its just a hunch.
This is somewhat long, but it details how that I came to my knowledge; through experiencing problems and solving them rather than having sufficient knowledge in the first place. This means I still have limited knowledge in this area, and your problem may not be the same.
But sometimes breaking things helps increase understanding...