I thought that too, I've been serching for solution for two days)) and I actualy did!!! So the problem was in spring bones. You see, I've rewached their tutorials for the hundredth times and in the one of the tutorial called "EPS Import and Animater character setup" he says that you have to live one bone UNASSIGNED. But, on the other hand i've wached their video with the tree, he makes it move like it's windy and all tree bones was assigned and everything works anyway.

Yup I'm seeing this as well. I bought this program with the intent of using this feature pretty heavily. I noticed that the bones with spring on them will simulate to the wrong position and when I click on them they snap to the keyframed position. Clearly a bug. 

I'm also having this problem, i've tried everything people sagested here, nothing works.

So did you find a solution to this?

I've not tried anything yet save for making bouncy ponytails and they react to being key framed to match the head motion.   That said I've not tried to animate individual bones in the prop.

It seems if I rotate and translate the entire object from it's hot point all the motion and spring action works fine. 
If I manipulate individual bones though it doesn't seem to remember the keyframes when previewing/rendering.
Though while adding the key frames via the Prop Key Editor all the individual bone manipulations DO show the proper actions in real time.

I think this may be the same issue as reported in an earlier post about motions made in the Prop Key Editor not rendering.

Did you remember to group the bones by checking the box on the lower left?  They must be grouped in order to spring.  I'm doing this from memory but I made that mistake a few times before remembering to group. 

Spring bone Props - More Testing
So after More Testing this is what I have found,

A Prop rigged with spring bones will only playback in the editor if:
1. The Spring Bone Editor is Open
2. You have the Track with the spring bones on it selected
3. In :- Edit / Preferences / Motion : Simulate Spring Physics in playback is UN Checked (All other boxes are Checked)

Then hit play button - All works ok :)
HOWEVER - Exporting either a video or PNG sequence the spring bone effect is lost ?? :(
Guess my jumping birdie will have to make do with a rather rigid branch for now
Thanks

I hope this is one of the know issues with CTA5 they are trying to fix,

I have spent Hours trying to resolve this weirdness, Spring bones work fine when scrubbing through the time line but won't animate when play button is pressed
I have tried rigging my asset as a prop, as a free bone actor, messing with the Motion preferences...

I figured it was just me not knowing what I'm doing but it sounds like a real issue, perhaps I'm not going mad after all.

At one point I thought I had cracked it, but this morning after deleting the part I can't repeat it ARRR! very frustrating !
At this rate I'm gona dust off ToonBoom again :)
Please post again if you have any joy getting it to work or have more workarounds
Thanks