Couple of things that change when you change orientation of a part. First most obvious thing is it is slicing the model from bottom to top and so the shape of the slices it gets will change depending on how you rotate the part (ideally typically want to print things like a cup sitting upright open side up on the bed because it is always building upward and can deal with overhangs of up to around 45 degrees without any support material underneath.
Can see in the screenshot above in slic3r (my current slicer of choice) it shows in the preview mode that the green parts are support material because I selected to add support from the plate only it will only add support there and not on top of the part, can see the blue parts in the top of the circle will sort of be printing in air it marks those as "overhang perimeter" (see legend in top left).
There are stress test models you can find that will check various sized holes and bridging capability (how far can things be spaced before the plastic just falls into a hole rather than gapping between two points in the air).
Couple other things that change when rotating the model is the infill pattern is usually aligned "globally" based on the build plate so rotating 45 degrees when you have a cross hatch infill will cause the infill to line of up with the part differently resulting in some change in rigidity of the part. Can see the infill in red below and the supports turned to "everywhere" adds more green support material in to fill in the hole so the material up top has something to sit on.
Rotated 45 degrees
Can see both the infill and support material maintain their orientation based on the global space not based on how parts are rotated.
---
One other thing to add having a "part cooling fan" or a fan blowing down on the parts just printed helps a lot with regard to keeping shape especially on tall thin things, perhaps this is what you were running into.
