Support pillar knocked off by hotend?

I'm trying to print Star Lord's mask based on the STLs provided in http://www.therpf.com/f78/star-lord-helmet-accessories-helagak-208660/

I started with the face mask part. Here's the part (left hand side) and the way it should be printed with support material (right hand side):


Notice there are two "pillars" that are supposed to support the top left and top right tips of the mask. The right hand side preview is not very accurate (e.g. I'm using a raft), but you get the general idea.

When I tried to print this, one of the pillars was fine (up to the point where printing stopped because of a system reboot, but that's another story). The other pillar started fine, but a few hours later I saw that it was knocked off, and not there anymore:


On the left hand side you can see the support pillar (not focused that well, sorry). The pillar doesn't look very accurate, but it's standing (it's not even half as tall as it's supposed to be in the end).
On the right hand side, the pillar is missing, and a lot of hanging threads are printed in mid air.

What might be the cause of that?
I followed the extruder calibration instructions, and I'm calibrated quite well.

Some technical details: Printed on Prusa i3 from Makerfarm with PLA 0.35mm at 185/60C, 0.2 mm height, 40mm/s general print speed, 20mm/s first layer, 30mm/s outer shell, and 120mm/s travel speed. Sliced with Cura 14.09.

Thanks.

I don't print PLA often but I recently had a problem printing a box with holes and near the top of the holes the hotend started to crash into the printing as it was curling upward. It's likely this is what happened here, the support is thin and it curled upward and the hotend then runs into it. While I have not fully tested the theory I was told to turn my fan down or off as it's cooling too quickly and this causes the upward curling. My next item I printed had a small hole so I turned the fan down from 100% to 60% and there was no curling but it was a much different structure so I am not sure if it was the shape or the fan.

Is it possible that things are cooling down too fast without cooling?
I'm not using a fan at all.