Factories can be complex, and there's a lot of potential reasons why you could be losing money. Key factors to look into are Output, Input, and factory budget.
If you go into your factory window and mouse over the item the factory produces, you'll get a nice little window showing you the production output/throughput. In there, some key things to check ore the efficiency values from clerks and craftsmen, as well as the maintenance goods the factory needs. A lot of factory losses can be chalked up to lacking maintenance goods. Remember the Synergy bonus from building a factory in a state that also includes the required inputs.
If you mouse over one of the required input materials, you'll see the input window. This window pretty much shows the same details as the production window, but includes the bonus you get from Capitalist, and shows you the stockpiles you have of the required goods.
You'll want to see as much green in those two windows as possible. The higher the output and throughput efficiency, the more goods you can produce, and the less input goods they require, which saves you money.
If you mouse over the factory profits, you'll see the budget window. It'll show you what the pure income of the factory is, what the costs of keeping the factory running are, and the total available budget remaining to float the factory until it's bankrupt and closes.
If you're losing money on a factory, the bottom line is your pure income (money you made from selling produce) is less than the cost of input materials and wages combined. You can't make money if nobody is buying your produce, or you can't afford the input materials to make it. Remember too, if you're the little fish in the industrial world (Low ranking nation), you'll be the last to purchase inputs. Also, the big powers are often self sufficient, so they won't always being buying your produce, meaning a lot of it will go to waste. If the problem is a lack of sales, you can always buy the goods yourself and stuff them into the stockpile. When demand is high, sell the goods later.
This seems a good spot for this tutorial again:
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