I thought initially that it was an issue with z-indexing and that the date picker was being displayed, just behind the dialog containing the table. Working on this assumption, I spent a while fighting with z-index settings in the jquery-ui css file as suggested in various online postings.
After looking at my code though, I realized that I was running this code after updating my table to enable the date picker on new rows:
1: this._editor().find('.DateEntry').datepicker(opt);
The problem was that I wasn't deleting all the rows in my table and recreating, I was only updating a subset of rows and adding a few new ones. Thus I was calling the date picker function on an element that had already been enabled as a date picker. This prevented any elements from being made into date pickers.
Moral of the story, never call datepicker() twice on the same element. Bad mojo.