In both cases, the same projected coordinate system is used, only the profile bounds differs.
And I was able to reproduce the problem with earth files:
Chicago_Projected_LargeArea.earth -> OK
Chicago_Projected_SmallArea.earth -> NOK
After a bit more investigations, the problem appears when reducing the ymax value of the bounds:
osgEarth::Bounds(447000., 4637000., 450000., 4639650.); -> OK
osgEarth::Bounds(447000., 4637000., 450000., 4639600.); -> NOK
Reducing xmax value has no impact.