What is causing the walls of my prints to separate?
I have faced the same issue if it concerns just gaps between the walls (to the point you could put a nail in between the outer and inner perimeters, so clearly the perimeters were not bonding), for me this was fixed with proper tension of the belts of my Prusa i3 clone, and for my other (CoreXY) printer reducing the friction of the X-Y system. Both help position the head better for proper wall adhesion.

Now that you have posted a picture of your product I do not think the above is applicable to you. Your print looks as if it has an under-extrusion problem as the lines on the faces are clearly not touching, you see the diagonals of the layers beneath. This under-extrusion also may contribute to the vertical wall bonding problems you mention. To fight under-extrusion you need to check a few things:


Be sure the slicer has the actual filament diameter as mentioned on the box, or measured at various points (if it varies, take the mean value).
Check your extruder setup to see whether you have play or friction preventing filament to extrude freely.
Also check whether your extruder gear is not loose, re-tighten the grub screw.
Final step is calibration. You want to be certain that when you demand 100 mm of filament to extrude, you actually extrude 100 mm. Put a mark on the filament and extrude 100 mm using a tool like Pronterface or Repetier-host. If this is off you should readjust the steps per mm in the firmware (if you are able to do so), or increase the extrusion multiplier or flow in your slicer.


Please look here or here for more information.