Ganesh is correct..you need to do an Examine Geometry check first (there is DATA CONSISTENCY check in the check list also.) If this is an already imported geometry then it might be due to some translation issues also (overlapping edges/Botched up corners etc.).
You can also use optimize on the body to refine the topology and then check if it still gives you issues.
I have a feeling that this error is not geometry related. I ran into something similar when working with a file from an outside source. You should really contact GTAC with the file.
I have gone through the part file. There are some CONSISTENCY CHECK failure and Optimize was not able to get rid of it.
I used HEAL GEOMETRY with some success but there are still some issues with the topology which can not be done directly...Either you need to redo the fillets/blending once again (first need to delete the blends ) or you can try reimporting the original file.
Lastly i would request you not to share the part files directly (in case these are confidential to you)...GTAC (as Ben asked for earlier in this thread) will be the best choice to share this part with and get it rectified.
The fact the part you are starting with already had the "_hg.prt" name in it, tells me someone probably already tried Heal Geometry on the original part before you got it, and hence knew there was an pre-existing issue at that time (and further that Heal did not completely fix, or perhaps made worse?).
I suggest that, if possible, you go back to the original part, before the first round of healing, and try to fix some of the issues that Kapil pointed out there, rather than trying to do additonal work on a part that's already been massaged a bit (assuming it's a part you have access to).