“Is the main problem simply the reduced price of output (due to competition with large scale industrial agriculture), rather than other factors (such as potential increased costs of inputs, degraded soil quality, access to water).”
It's mostly the market price of outputs. As was stated in the OP, producing a gallon of milk costs $1.90 or thereabouts. The cost in the grocery store is $2.59 in my area this week. This price has to cover not just the farmr's costs, but the shipping, packaging, and grocery store overhead. The farmer is lucky to break even, and often doesn't. I've read elsewhere that to guarantee a dairy farmer a living wage, without government subsidies, a gallon of milk would have to go for closer to $5. If you want organic, non-feedlot milk, that cost is even higher.
In my sister's case, our 300 acre farm can support around 75 breed cows, which means you could expect about 65 heifers and steers born every spring and sold every fall. These will be around 1200 pounds, at a “dressing percent” of 63% which means you get a 750 pound carcass. 490 pounds of this will be meat - let's call it 500 as a round figure. So she could produce 32,500 pounds of beef a year. The vast majority of this, over 75%, is going to be ground beef. A small fraction of it will be filet mignon.
If you figure that her business expenses are going to be in the neighborhood of $150,000, which is going to include equipment upkeep, fuel, fertilizer, seed, feed milling costs, farm maintenance costs, vet fees, medication per animal, and so on. She is going to need $50,000 in income to support her family, so that means her price per pound of beef would have to be about $6.15. Not including the cost of butchering, transport, auction fees, and all of the upstream costs (packaging, grocery store overhead and profits, etc). Now if you walk into your grocery store you will find ground beef commonly going for $5 a pound or less.
The 4-H says it costs about $7 a pound to produce beef, so that's a pretty good estimate.
And note that this does not include buying new equipment. A new tractor of a size that would let her bale hay starts at $50,000. Paying to have the farm re-fenced would be somewhere between $50,000 and $100,000 depending on specifics. It also does not count all of the horrible things that can and do go wrong farming. If she cuts hay and it gets rained on before it dries, she loses that crop. You get three hay cuttings a year. That's a third of your hay crop gone, which means you have to buy hay. If there's a drought, you might have to buy water by the ton and have it trucked. If you get an outbreak of hoof rot, you lose a significant number of your animals and a significant amount of your pasture has to lay fallow for years until the pathogen dies. The number of horrible things that can go wrong that are beyond your control means that the above prices don't provide enough financial cushion to make it through a bad year or two.