I just had confirmation of the support service that it is certainly a bug. 

The problem comes from the use "look at camera" ... as soon as one uses this function, it is not recorded in Motion Plus and even less in a file FBX during the export. "Look At Camera" is nevertheless a very useful and essential function during animations. The bug has existed since TonyDPrime has postponed it in 2017 ... I hope that the Dev Team can solve this annoying problem. While waiting for this correction, I strongly advise those who make their renders in a third party program (such as Unreal) not to use this function and to use Face Puppet or Face Key in order to remedy some problems related to the "look" of their characters.

Despite this, nothing will change the fact that Iclone remains one of the few animation solutions to allow independent artists a professional quality, an immeasurable time saver as well as an important workflow.

I have the same problem... (Iclone 7.4 pipeline) Any "Eyeball" animation (expression, face key...) won't export in my FBX file... thank for your prompt support.

I'm having the same problem. 
I understand that this issue is supposed to be addressed with the "Bake Constraint Key" option, documented here: http://manual.reallusion.com/iClone_7/ENU/Pro/Default.htm#iClone_7/Pro_7.0/08_Animation/Baking_Constrain_Keys_into_iMotion.htm?Highlight=bake%20constraint%20key
I understand that, in theory, I should be able to have a character look at a camera or other object, then check "Bake Constraint Key", then collect the clip and add as MotionPlus to library, then apply that to a new project, and have the character continue looking in the same direction.
Unfortunately, it doesn't seem to work properly; when I apply the MotionPlus file to a new project, the eyes are looking in the wrong direction.
I made a video of it here: https://drive.google.com/open?id=16N66g4A6SGsuanlgtxcQopS1RtSIx7EK
Description of the video: I created a new project with the default avatar, applied an animation, and made her look at the camera. I then ensured "Bake Constraint Key" was checked, then collected the clip and saved as MotionPlus to library. I then opened a new project with the default avatar and applied the newly saved animation from the library. She is not looking at the camera, and her eyes are looking off to the left (her right).

Thanks for the opportunity to further detail my finding for the iClone community.
Also, I have made an additional discovery, if you try to export such a motion sequence to a iMotionPlus file, "it" will also not work.  
My "it" is a Direction Puppet Head Movement + Face Key Expression + Look at (Panning) Camera 


STEPS TO REPEAT PHENOMENON

1) create scene (TEST SCENE 1) with 1 CC2 avatar, face close to Preview camera
2) set up scene with camera, and have avatar "Look At Camera"
3) set Look At Weight bias to Eye (extreme left side of slider)
4) set up cam to pan, say at a 45 degree angle, from avatar's right side of face to left during the course of the sequence (ie frame 0-1800)
5) Use Direction Puppet tool to add a movement to the head (ie nodding left to right in a circle pattern)
6) Use Face Key to add expression action to the face
7) Use Collect Clip in Timeline to capture the motion as an iMotionPlus file
8) Save TEST SCENE 1
9) Export avatar & camera as an FBX file (ie to Max, Maya, etc, as "TestScene1")

To Test iMotionPlus
10a) Right-click on avatar and delete object animation
10b) confirm that there is no Look At Cam setting applied, but confirm that the panning camera view is still active, so that avatar is in cam's view entire sequence.
10c) Import the previously saved iMotionPlus motion onto the avatar
10d) Play the sequence through, in my tests the character will show the (a) Direction puppet head motion and the (b) face key expressions, but will not be (c) looking at the camera

To Test FBX
10a) Import TestScene1 to Max, Maya, etc.
10b) View scene from the imported Camera 
10c) Play the sequence through, in my tests the character will show the (a) Direction puppet head motion and the (b) face key expressions, but will not be (c) looking at the camera


*I found if it was a pure pan Look at Cam + with Direction Puppet head motion, but NOT the Face Key expressions, it actually can be saved as a iMotionPlus/exported as FBX, and retain the Look At Cam action.  But, once you attempt to combine Look AT Cam and Face Key, it seems the issue arises, as the Look At Cam is removed.

THX!