Rear differential

If you have a clutch type sure grip unit, you must remove the center thrust button to run green bearings. That might be your issue.

OR if it is a cone type sure grip, the cones and side gears are probably out of alignment. They must be aligned properly in order for the axles to fully engage. My guess is, it's one or the other.
I tore it down late last night and found that I couldn't fully seat one of the axles because the inner splines were not aligned, which would prevent the shaft from fully engaging, so hopefully, this takes care of the issue.