My daughter had this same problem - straight prune jiuce at 8 weeks worked wonders!!
But the dr also thought she might have had a "german sounding" condition where the muscles at the opening of the bottom do not work, until either it sort of explodes out or if a suppository (baby size!!) was put there it effectively did what the muscles wouldn't do & she went!! If this had been the problem an operation would have been required.
Another cause of her bowels not working & this is the reason, we finally discovered about 4 months ago (or rather our daughter did by going on line & searching - she'll be 16 this month & has suffered severe pain all her life from this) she has irritable bowel syndrome & so needs a specific carbohydrate diet & things have now improved greatly - so ong as she sticks to what she can eat.
Hope by now all is fine if not & if you do want more details pm me.