Answer: An excellent question. This issue has bothered me as well, and I have not found a single Sefer that address the question directly.
A little background. While it is always preferable to make a Beracha on a complete item, it is especially critical to the Mitzva of Lechem Mishan for Shabbos and Yom Tov to use a whole loaf of bread. Therefore, while during the week one should make an incision in the loaf before the Beracha to indicate the location he intends to slice, on Shabbos this should be minimized (whether this Halacha applies at all to our Challos today is a separate issue). Even on a weekday, the maximum permissible incision to preserve the "whole" status of the loaf requires one to be capable of lifting the entire bread when gripping the prospective piece.
The question is, is this a general rule that an object is incomplete if any section of it is incapable of supporting the weight of the entire item?
I would tend to be inclined that it is not. I suspect that this Halacha is specific to a situation where a break or separation has commenced, and it merely quantifies the maximum size considered attached. However, when the loaf is intact but merely weak, that infirmity does not deny it from wholeness.