How common is it for women to drop out of graduate school because they have children?
My wife and I both started graduate school, in STEM fields, in Ph.D. programs, a bit later than most.  

Due to this, we decided to have children during graduate school.  Note that I am in the USA at the one of the top programs in my field at an RU/VH university.

A few negative points are 


As a graduate student, you are expected to work full time, but you are not paid enough to afford daycare costs for young children.
For the first year of the child's life your research output will be severely limited.  Some PIs may not like this.
After children, you have to be very focused and disciplined to continue, time scarcity increases a great deal, and time is already scarce even if you are a single graduate student with no life.
My wife had severe morning sickness, which decreased her research output. Pregnancy complications can affect your work.
After you have children, being poor really starts to become a burden.  After all, we want to give our children a good life.
Your time in graduate school will be extended.


A few positive points are


Due do the nature of research and graduate school, hours are very flexible compared with a typical job.  This allows for juggling of schedules when needed, etc. which is very helpful to us.
The Ph.D. is less crucial than a post-doc or a tenure track position, so I would posit that there is less risk to have children during graduate school as opposed to other crucial academic career milestones.  However, the caveat is that graduate students receive the least money.
Many PIs don't care what you do, as long as you make research progress. This makes it easy to work around a young child's needs. 


The way that we have dealt with this situation is by 


Having understanding PIs who also have children, and are flexible.
Acquiring some debt (that we wouldn't otherwise incur) and I've done some lucrative consulting on the side.  The consulting has however, increased the time to graduate in my program.
Being very disciplined in our schedules and having our children in daycare/preschool so that we can work.  This is very expensive.
Not having a social life (but graduate students aren't supposed have those anyway right?).


To answer your question, for us it is working.  However, I do know a few other couples who are doing this, one other couple is like us with both parents in graduate school, but nearly all of the others have only one parent in graduate school.  

From my perspective, it appears that women leaving academia due to children is becoming less of a problem, but is still large, and unsolved.

Note : our university does not provide daycare to graduate students.  They do provide a $1000 annual subsidy, but our daycare costs are $10,500 per year.  These costs decrease for preschool, but are very expensive for the first three years.

Second Note : My graduation time will likely be right around the 6.5-7 year mark, I had my mother die during my time in graduate school, and we have had two children, so the actual time increase wasn't obscene, but I already had an MS in Mathematics coming in and was expecting to finish in 3-4 years.  My wife entered her program straight from BS and will probably finish in 5.5-6 years.  

I would also like to say that the needs of the child and the lack of sleep disproportionately affect women in this situation, and this is a biological necessity in the first 2 years of the child's life.  For this reason, equality for women in academia does not mean equal treatment, it means providing for the ability for women to have children if they so please, without it impacting their career! This necessitates providing more support for women and families to have careers and children.