First of all late term abortions are rare. The Guttmacher Institute reports 6.2% of abortions were conducted between 13 and 15 weeks, 4.2% between 16 and 20 weeks, and 1.4% at or after 21 weeks and 0.08% after 24 weeks. The Institute estimates that 1% of all medical terminations of pregnancies are done at or after 21 weeks, poor prenatal diagnosis etc. But that's not the whole of the answer. In 2008 GI did a study on late term abortions and found the majority who had a LTA for a non medical reason were young and poor without higher education, many were African-American. You had teens who waited too long because they had no adult to go to and were afraid to speak of the pregnancy. You had women who were unable to quickly come up with the money for an abortion. Others didn't have access to a provider. Some had multiple life crises that didn't allow them to make timely decisions. There were even incidents of young women who weren't even aware they were pregnant until it began to show.
Then the solution is simple. Increase education and awareness, pass legislation to make the choice available and possible, and in general fix the underlying issues that lead to a late term abortion.
The fact that money is ever an issue in terms of medical care simply disgusts me... That we would put a price on health confounds me. We, as a nation, have the resources to provide a top level of care for our citizens... But because health care is a for profit business opportunity instead of a right, proper treatment is out if reach for many, and that which they can get still often leaves them indebted