Girl does NOT want to poop - AT ALL

My daughter just turned three. She has been potty trained for almost a year, and for the most part it's gone very well. The problem is that she doesn't want to poop. This is not to say that she will only poop in a diaper; she simply does not want to poop. She ends up holding it in, it's gets bigger and bigger until it hurts when it finally *has* to come out. This in turn makes her not want to poop even more.
We've found several solutions: high fiber cereal, warm bath, prune juice. I've tried explaining that it's OK, everyone has to poop, that her belly will feel better once she's done it. I've tried reading books to her, even bringing the laptop in the bathroom so she can sit there and watch a favorite video. Each of these things has worked once, maybe twice, until she figures out "that made me poop!" and she learns how to overcome them.That girl can drink 1/2 glass of prune juice and still not poop.
On those occasions when she has pooped in the potty we celebrate and give her a "special treat" and tell her what a good girl she is. She is happy, then, but she goes right back to her withholding ways.  Eventually her little body can't take it anymore, and she ends up pooping in her sleep, when she's relaxed and can't hold it back anymore.
Her father and I are patient. We're not obsessing over getting her to go in the potty. We just want her to GO. We worry that one day she's going to end up impacted and will need a trip to the hospital. Is there any help out there for a girl who doesn't want to poop at all?

[AnnieBrooke]

I think you should stop talking about it and stop trying things, and keep her in diapers or pullups.  The amount of 'holding it' she is doing can enlarge her colon and give her serious problems with encopresis.  I would rather have a child who is still in diapers at age 4 than have a child with encopresis.  Please just leave the whole subject alone.  She'll get accustomed to the idea that her friends poop in the toilet, especially if she goes to preschool at an age where some kids are still in diapers and some are in underpants, and pretty soon it will click for her without your urging.

[rahwher]

Thanks for the response. Unfortunately, the problem isn't whether she's wearing diapers or using the toilet. Either way, she simply refuses to poop. If I could put her in diapers and she would actually poop, I'd keep her in diapers for as long as it takes.

[AnnieBrooke]

There's a really good article in the (I'm pretty sure) March, 2010 Parents magazine called "When Your Child Just Won't Go" that explains encopresis, and the treatments for them are quite long (stool softeners for a year and things like that).  It is written by a doctor, who comments that a lot of pediatricians are not up on the proper treatment of encopresis at all and don't have the child treated for long enough periods of time.  It might be worth a read.