I have made the recipe a number of times (at least 14).  For reasons I cannot fathom, the braids pull apart (or separate) in places on the top during baking.  Otherwise, the challah comes out fine, if not fantastic.

( http://www.realbakingwithrose.com/2006/03/my_new_favorite_traditional_ch.html )

I am using the lowest shelf in the oven and a double baking sheet - the lower sheet is heated while the oven warms up to 325 deg. F.  In all other respects, I am following the recipe exactly.

Two additional pieces of information.

1) I am placing the dough in the refrigerator overnight after the second rise (and 2 more business letter turns). Time in the refrigerator is approximately 20 hours.

2) Upon closer inspection, it appears that the outer braids have broken in places (i.e., cross-wise), so they are not continuous through the challah.  See the attached photos.

Perhaps I am doing something with the dough that decreases its elasticity.

I would appreciate any suggestions or hints. Thank you.

Joel, for clarification, are you refrigerating the shaped dough or do you shape after it has been refrigerated?

I refrigerate the dough before shaping and proofing (“for best flavor development”); the dough has already gone through the first and second rises.  It is the step at the end of section 2 in the recipe, just before the table titled “glaze.”
  http://www.realbakingwithrose.com/2006/03/my_new_favorite_traditional_ch.html
According to the instructions in the recipe, the dough should be given two turns and then refrigerated.  Then, after cutting into small logs (before shaping), the dough sits for 20 minutes.

In looking again at the bread, and in light of a comment on another site, I wonder whether the braids were too tight such that the rise of a braid from below literally split the braid on top.  The ropes are much thicker in the middle and perhaps the expansion caused them to cut right through.  Perhaps more uniform and less tightly woven braiding would help.

I am having the same problem with my Challah.
I make my dough in the bread machine. Then I braid it.  It doesn’t seem to matter how long I let it rise after braiding (I’ve even tried not letting it rise at all!)
Sometimes it pulls apart a little, sometimes a lot. I tried rotating the pan half way through, because it seemed to split more on one side than the other, so then the whole top pulled apart.