Let me clarify the situation: you are her teacher, not her parent. This makes it your job to explain matter to her, and it's the job of the parents to prepare her for that.
As you have stated:
Her father said she is sensitive. I was asked to do more praising and encouraging from her parents.
This is not your job! Not at all!
Let's face it: crying is an enormous time and focus waster: when a person starts crying, he or she looses his or her focus for quite a long time, so it should happen as less as possible.
I remember that, also at the age of 12, during one lesson, I've been crying too. As far as I know, the teacher did not even speak to me, he just let it happen, and I never had any bad feelings towards that teacher for that.
I have the impression that the parents are not dealing well with their sensitive child and let the burden on you, and that's not the way education is to be done: it's your job to deliver the matter and it's their job to make her ready for dealing with that matter.
Oh, if you think I'm being harsh here, just think about this situation: I imagine you have a regular class of about 20 students, and you are planning of adapting yourself to the "special" needs of one single student. Another student might notice that and invent a "special" need for him- or herself too, do you see the snowball effect coming? ... at the end you'll be dealing with "special" needs that much that you won't be able to teach your class anymore.
Does this mean there is nothing you can do? Well, the easiest you can do is increase praising of every student in your class. Like this, her need to praising might be fulfilled (or at least reduced) and you don't make an exception for one student. But don't go further than that.