Losing money is important is indeed a peculiar thing to say, though there's nothing wrong with the sentence's construction. It's simply extremely unusual for circumstances to arise where this would be a true statement.
However, I do have an example. This fiscal year, I had to reduce my tax burden by lowering my gross income below a certain level. The only way to do that was by incurring capital gains losses (i.e. making bad investments), so for a time, losing money was important to me.
Important means of great weight, rank, significance, or value; critical or pressing, and need not necessarily be emotionally positive. It's true that Hitler is an important figure in history, because his actions had a huge impact on the world, but it's also true that history (rightly) views him and his actions extremely negatively.
Earning money is important has positive (emotional) connotations because it's a positive (not negated) statement, and we generally view earning money as a good thing. Both not important examples express the idea that their subjects are not very desirable; one could take or leave earning money or losing money. There's no major positive or negative (in the emotional sense) connotation here. Often when we say something is not important, we mean that we don't have strong feelings either way about it.