My observation wasn't accurate enough.
The looseness came from the fact that the N-SMA bulk heads were slipping on the black plate.
This is actually what Suresh pointed out (see here). So the thickness of the black plate doesn't matter in this case.
Somehow I was able to tighten the bulk heads using two wrenches and I think they are now tight enough so that the heliax's heads don't move any more.
I found that all the Heliax cables landing on the bottom of 1Y2 were too loose.
The looseness basically comes from the fact the black plate is too thick for the Heliax cable to go all the way. It permits the Heliax's heads to rotate freely.