Lay flat does not work on small objects.
How small?
What kind of shape do they have?
Can you attach the file - or if that's not possible: a screenshot?
The part was no more than 2mm in width. I discovered that if I took snap off it worked.
Problem reproduces easily with a cube scaled such that either X or Y is 2mm.
Problem goes away if total object is scaled to be larger.
This bug is genuine.
I also found the problem with a 10x10x2mm cuboid (Z was 2 mm, the other two dimensions were 10mm).
Our project manager just removed this from our planning though, because the issue is more than 12 weeks old.
Probably due to this: https://github.com/Ultimaker/Uranium/blob/master/UM/Operations/LayFlatOperation.py#L54
The idea there is that if you have a large high-poly model, you probably don't want it to balance on a tiny triangle when there is a larger flat plane.