L.B.
It sounds like she has had a painful bm at some point and is holding her poops. I had exactly the same problem with my son and took him to the DR. where I got no helpful info! I finally found some good info online that worked for us.
First of all, you need to make her bm's really soft so that they don't hurt when she finally goes. Give her 1 or 2 tablespoon of mineral oil in the evening mixed with a little OJ (or other fruit juice). I told my son it was tummy medicine so that his poops wouldn't hurt and he took it easily (it's tasteless anyway). Also, start mixing in a tablespoon of fiber (like Benefiber) into everything that she drinks during the day. Within 24 hours she should have a BM. If she won't sit on the toilet, put her in a diaper when she needs to go and tell her that it won't hurt her when she has her diaper on.
Add natural fiber to her diet like popcorn, fresh fruit and whole grains if she will eat them.
Don't pressure her to go; she will not be able to hold her bm's if you give her the mineral oil and fiber and let nature take it's course.
Keep this up for at least a month after she starts going regularly, and then slowly ease her off the oil and fiber. If you see that she is not going every day, start her again but on a smaller dose of fiber and oil.
One thing about the mineral oil, it can prevent vitamin and nutrient absorption, so don't give it at mealtime.
Good luck!