There are many reasons for glue to fail. If the furniture was originally put together with Hide Glue, then a change in temperature or moisture in the air, could cause the glue to fail. Hide Glue is very strong, as long as it is kept in normal indoor conditions. But it is activated at high heats so if you leave the chair on the porch in the summer, the glue can be activated and then while the joint is soft (and not clamped) it can become loose and fall apart.
Other joints fail because a bad or experimental glue was used. In the early 1900's a Lignin glue was used and it has a very high fail rate. We get furniture in fairly often that originally had this kind of glue used. Joints can also fail because not enough glue was used to penetrate the surrounding wood fibers. If the chair has had a prior repair attempt, sometimes an in-experienced repairman will not clean the old glue off before applying new. The glue then just bonds with the old (already failed) glue, instead of to the actual wood.
Diagnosing why a joint failed can almost seem like diagnosing a medical condition. It really does help to know the furniture's history. But regardless of why the joint failed in the first place, a skilled, experienced repair specialist can put the furniture back together, regardless of how many pieces it is in. The new bonds they create between the pieces should last well into the future. When you go into a shop to get your furniture worked on, be sure to ask lots of questions so that you know what your glue options are, what each glue's risks are, and get a good sense that they know what they are doing!