Why does soda bread preserve less well than sourdough or yeast based bread?
The only major difference between the two is moisture, soda bread tends to be wetter than yeast breads, more like a cake than a yeast bread in many ways. Bread gets stale partly because of the action of moisture, and mold needs moisture as well, so because soda bread is more moist than many yeast breads it will get stale and moldy faster than most yeast breads. 

Keep in mind that just about all breads no matter how they are leavened are best eaten fresh, although they will keep for several days. This includes soda breads, which will keep for much longer than a single day. Stored properly you should get 3-4 days out of it. So the recipes saying that soda bread will keep for a day are not really that accurate.