I have had this issue for ages in Unity and can’t seem to fix it. When I import an fbx file with animation, then split the long animation clip up into smaller pieces, it always pops. If I go into the animation curves (which are read only) I can see that Unity is adding little bumps and curves on the sub-frames and it’s causing noticeable hiccups in the animations.
Does anybody know how to fix this problem?
So you have the exact same issue as me I guess:
Any ideas on why this is happening or how to fix it?
Nope. Nothing yet.
Will keep you updated if I learn something.
Please do the same for me.
Suggestions from an artist who uses the second most popular, animation package Max. 
First - Try to reimport the fbx back into your 3D package then re-export - then bring into Unity. Any change to the curves?
Second - Try to add one key before and one key after the stepped keyframes, then export to Unity. Any change to the curves?
Not sure if these attempts will result in a solution.
Sorry for your troubles - I’ve seen this before with Maya content, unsure why.
cc’d to the other thread also.
When I try to re-import the fbx into maya, it is just in a bind pose, gives a bind pose warning that it doesn’t exist, and no animation frames are present. The only way they will play is if I manually bake the keyframes to the skeleton, but I choose bake on export so it should be fine, as the animations play in Unity.
I should mention I am using Maya 2014 and the 2014 version of the fbx exporter…maybe reverting to an older one might help?
I think what is happening is that Unity cannot break the tangent cleanly like Maya can, it is anticipating the next curve or coming off the last one and the handle controls both sides of it, instead of just one.
Here is the best solution I could come up with to stop the popping in the curves…
I spaced out the keyframes between different animation loops, so instead of one frame between them in the timeline there is a gap of 5 or 6 frames. I selected the whole skeleton hierarchy, baked the animation manually in Maya, and deleted the rig, so only the skeleton and the mesh were left. Then I exported them into Unity and turned off the “resample curves” option. This removed the pop I was getting in the animation. The most important thing seems to be leaving space between animations. It’s not exactly perfect, but it works.
As a side note, I get weird space flipping in the curves, where they are drawn as going to 360 degrees and back, but it doesn’t affect the animation. So strange.