I have intermittently had this problem with the Press.  It is an X-axis shift for me.  I caught it happening yesterday.  There was a momentary jam as it moved left, the belt seemed to bind and then it continued printing, but in the wrong area.  The rod was not evenly lubricated.  A dry spot in the center and almost goofy at the edges.  I wiped it all even (there was dark residue on the rod, likely from the melting plastic). Trying a test print now to see if this works.

Seems like the same problem I have. Maybe I should clean and lube up :-)

A couple of things. 
3.  I've had some troubles when printing  at very low layer height (.1mm) as there will always be some curl on the outside of objects and this can be enough to block the print head.  Have you tried different layer heights?

I had this too. I solved it by setting a z-lift value of 1mm. Slows the print down but it solves the problem.

2.  Have you been able to catch it in the act?  It is probably getting stuck on a lump of plastic which is causing either the motor to miss steps of the belt to slip.  I think that part of the issue with the honeycomb is that it will take a long time to finish a layer, so very hard if there are any imperfections as the extruder travels back over the previous bits.  Maybe setup a webcam taking picture at 2 second interval so that you can review where it is getting stuck, if that's the issue.

3.  I've had some troubles when printing  at very low layer height (.1mm) as there will always be some curl on the outside of objects and this can be enough to block the print head.  Have you tried different layer heights?

See attached picture.

Any ideas?