Four year old suddenly REFUSES to poop.

My 4 year old daughter has been potty trained since 18 months, and has had no bathroom issues since then. All of the sudden, within the last month, she has decided not to ever poop again. She becomes terribly upset when she needs to poop, says that she is afraid of the "bad poo-poo" and that she doesn't want to let it out. She is upset a large portion of the day, whining and crying, all in an effort to retain her bowel movement. The routine has become 4 or 5 days of no pooping, and then having an accident in her underwear accompanied by hysterical crying and real fear. The stool is not hard at all, but a normal healthy bowel movement. (Just... a ton, by that point.) I have limited her dairy consumption, increased her fiber and water, make her drink a glass of prune juice daily, and yet the problem persists. We have also discussed the importance of pooping, and I have even explained in detail the body's process of passing food, complete with illustrations of the digestive system from my anatomy textbooks. She enjoyed the lesson, but ended the conversation with "But why do we HAVE to get rid of our poop? I don't want to!"
I fully believe that the issue is emotional (and MAY be due to her dad leaving three months ago for his 3rd deployment overseas) but I am at a loss to how to proceed. She is an otherwise stable, happy, healthy little girl.

[RockRose]

I agree that it probably has to do with her dad leaving.

I think since this is so recent,  just keep doing what you're doing,  matter-of-factly for awhile more.    It sounds to me like she's experiencing loss and doesn't want to lose anything more.

I wonder if doing something to acknowledge her loss of her Dad again - like,  daily drawing pictures for him or somehow otherwise daily feeling a ritual connection with him might help?