Foremost, I cannot say that the aspect is absolute. That is to say "women who see the baby on an ultrasound do not usually have an abortion."
So far, we've only had your anecdotal evidence, and with this the assertion of the type of pregnancy center in which you work. It sounds to me very similar to the catholic centers where I volunteered as a teen. To contrast this, I have also worked in a clinic more akin to a Planned Parenthood as well (in a state where counseling prior to abortion was required).
In both instances, my volunteer work lasted only a single summer (12 weeks), but included training, meetings, and some sessions (sitting in as a matter of training), though I mostly filed and greeted people in both clinics.
I found my experience in these to have two contrasting experiences around counseling:
A. In the catholic clinic, the women who were coming in were often stating that they felt they had no other option than to have an abortion, that they 'wanted' one. But, through the counseling process, it was largely their fears about not being able to care for themselves in pregnancy or their child after -- and the catholic group would gently draw them into the space where they would keep their pregnancies and provide the services that the women needed (from medical to adoption to services for child care/rearing, housing, etc).
I would characterize this counseling as encouraging, gentle, loving, but with a clear sense of what they wanted for the woman and child -- largely because they didn't provide abortion services, nor would they help the woman if that was the decision she made. They encouraged towards their POV.
If a woman was particularly unclear about the nature of her pregnancy and the child, then they might use an ultrasound to help her "connect" emotionally.
I do not think that this process is "wrong" in any way. I'm just explaining what I experienced. I felt that women were often "walked through" the ideology and perspective, until they came to the conclusion that the crisis center wanted them to have. If the woman wanted to continue with abortion even after this, then they would (kindly) inform her that she needed to go elsewhere, but would not tell her where to go.
B. In the other clinic, the women who were coming in had similar trepidations, but also seemed more certain in their decisions. They were provided with counseling, but instead of one idea being lovingly and consistently unfolded before them (the idea that it is possible to maintain the pregnancy, that there are options for child care and/or adoption), i found that it was more informational rather than supportive in any one direction.
This clinic, by law, had to provide information on adoption services, welfare and related services, and also provided maternity care (for free), so it was passing along the exact same information as the catholic center where I'd volunteered before. But, whatever the woman's ultimate choice was, they would simply follow through and "support" her in her decision.
The people who worked in this community, like red fox, were very caring about these women and their families, wanting to provide their best support and care, but without convincing the woman one way or the other -- toward or away from abortion. I don't recall a woman ever being offered an ultrasound to see her baby (as would happen in the catholic clinic and I would be asked to prep the room for that when it happened, or book the appointment for it), but if a woman asked, she would be given one.
This is largely a difference in method, drawn out of a difference in perspective. In the first, the child holds greater importance to those who are helping, and in the second, the mother's choice (or you could say the mother) holds greater importance.
In both instances, I always felt that both parties were compassionate toward the mother and the child, though those on each side of the "sense" would see the other as not valuing the other (i.e., the catholic clinic would say the other one did not value the child enough; the other clinic would say that the catholic clinic did not value the mother enough).
On a personal note, I say that both cared for both "enough" -- but weighed one over the other in each case -- and provided services based on that perspective.
In regards to why women would be convinced, I am asserting two positions in this regard:
1. If you are working in a clinic similar to the catholic one, the intentional process in the counseling is to make certain that the woman sees the gestating infant as a child, a person, a baby. If it takes a ultrasound to get to that, then they'll use it. And, I found that -- in those clinics -- most women were deterred from having an abortion.
Was that due to the ultrasound? the counseling/education? where these women predisposed to it by choosing to come to this center first, as opposed to another center where they could -- more quickly -- walk in, get through the legal requirements, and get an abortion?
2. I believe that the intended process of this ultrasound is two-fold:
A. to provide more information for the woman;
B. to create an attachment for the gestating infant in the woman.
Part of what I am curious about is this.
In your clinic -- and based on how I see you expressing your experience, which mirrors my own experience in the catholic clinic -- you provide these ultrasounds and you get the result that you seek: women keeping their children. It might be what creates that attachment, as opposed to simply providing information. The reason I think this is because so much information was already provided to the woman in abstract ways (i.e., pictures, drawings, and descriptions of the gestational age of the child, plus things like "heart beat!" and "brain waves!" thrown into the mix as well. A lot of people focus on the Juno-aspect (from the film): finger nails! But no one gives a crap about finger nails. In our world, heart beats and brain waves mean life! And, so, the posters
read "abortion stops a beating heart" doesn't it? 
In the other clinic, if it is provided more dispassionate, informative way, the question remains as to whether the majority of women would be convinced or if it would simply provide another point of information.
The problem being, of course, that it may not be just a point of information for some women. It may be that it creates an attachment, and therefore the outcome that people desire. But if it's across the board -- there may be many women for a variety of reasons for whom this emotional attachment would be more risky.
From a legal standpoint, I question whether this is necessary.
Most of the standards already involve getting counseling, getting information about the procedure -- and as red fox pointed out form her experience, most women are already agonizing over this experience.
It would be far more difficult for these women to go through the ultrasound as well -- having already agonized in the extreme (as would be the case for me, were I forced to come to it) -- and I don't think this would be necessary.
So, to answer the question directly. . .
I think women who see the baby on the ultrasound (in your center) usually do not have an abortion because the whole process has been designed to create that outcome, the ultrasound being that last element to create a whole attachment to the child, while also providing support to the mother so that she can maintain pregnancy.
In a situation of red fox's clinic, it seems that the result may not be the same, though it is possible that more women may form an attachment and reconsider, choosing services over abortion.