By my observations, this cannot be true. Most women who get abortions are not deliberately pregnant; they are deliberately cooperating in baby-making acts by their husbands or boyfriends (having live sperm injected into their genital tracts) but not intentionally getting pregnant.
That's the disconnect. That's why contraception triggers more abortions than it prevents. Contraception has two effects: the pharmaceutical one, and the psychological-behavioral one. The pharmaceutical one reduces the likelihood that any individual act of intercourse will result im pregnancy. The psychological-behavioral one vastly increases risk-taking by both males and females, by creating a cognitive disconnect between sex and fertility.
The second effect overwhelms the first effect.
Thus contraceptives increase unwanted pregnancies. This can be verified by the fact that whenever a new group of emales become contraceptive acceptors, their unwanted pregnancy rate, nonmarital childbearing rate, and abortion rate goes up -- not down.
Excellent!
I have never encountered anyone who had an abortion because a contraceptive failed. I have, however, known of plenty who had abortions who didn't bother using contraceptives. I've personally heard statements to the effect of "Oh, I don't have to worry about birth control, since I can always just get an abortion." I've had men tell me that girls they were dating told them the same thing; I've read it in articles by those who are "pro-choice" (who, unsurprisingly, had at least one abortion).
The only place I ever saw that featured women claiming to have had abortions because of contraceptive failure was an article in Health magazine several years ago, where they featured a few women in this category. Unfortunately, the article's definition of contraceptive use was extremely generous. The only other source I've seen that contraceptive failure is a major contributor to abortion is the Guttmacher institute; given that it's a branch of Planned Parenthood, its claim is highly suspect.
There is nothing stopping any abortion client from claiming she was using contraceptives when she is asked about it; that is probably the biggest factor in the supposed high failure rate. Listen to someone explaining why she had an abortion, but without prompting her by asking about contraceptive use: in this situation, women do not volunteer that their contraceptives failed--in other words, they weren't using any.
It plays into the abortion industry's hands to accept their claims that a large fraction of their clients had their contraceptives fail. There isn't a lot of corroborating evidence, however. For one thing, if contraceptive failure was a major cause of abortion, you would expect the abortion rate to be the same across the board: there would be no difference between races, and the rate would decline with age in conjunction with fertility loss. However, neither of these patterns are seen: the differences in abortion rates between different races are drastic, and the majority of abortion clients are young teens. This tells me that irresponsibility is the major driver of abortion.
There are other pieces of evidence, as well. However, I have already written enough!
Well, except for one little thing: I have known of three women who did get pregnant despite contraceptive use. All three put their babies up for adoption. I do believe that one's views on abortion are the major factor driving whether one will endeavor to use contraceptives correctly, or will use them incorrectly--if they bother even using them at all.