What caused the sundering of Bree and the Shire?
Bree and the Shire, by all rights, should be closely linked.
The geographical divide between the two communities is small- on the East Road you could travel from the Eastfarthing to Bree a few days. That's not much different from the distance between Buckland to Michel Delving, for example. In addition, the settlements aren't that culturally different. Frodo and company seem comfortable enough after just a few hours in Bree, and likewise the Bree-landers take to the Shire-hobbits quickly enough. It's emphasised how xenophobic people in the Shire are, but I think to someone in Hobbiton, a Bree-lander wouldn't be so different compared to a Bucklander, and Merry mentions that contact between Buckland and Bree used to be regular (if not frequent).
Furthermore, it seems that the Shire and Bree did have plenty of contact historically. It's mentioned that travel between the two used to be more frequent, and the presence of 'Shire' last names among Bree-hobbits suggests intermixing there as well. The connecting road seems to have been maintained with trees planted along the margins. Nor does the trip seem particularly perilous, with the road staying well clear of the Old Forest and the Barrow Downs. In fact given time I would've thought that a strip of development would've appeared along the road, so that eventually the Shire and Bree would be merged into a single continuous settlement. At the very least an Inn along the road seems warranted.
However, evidently things did not turn out this way. We know that both the Shire and Bree are insular communities, so was this a case where they just willingly ignored each other? Given the hints of past connections, that doesn't seem likely. The sundering of communities seems to be a more recent development, and though the book remarks on this no explanation is given as to why.