I'd agree with pinksoil, sounds characterological rather than situational. At least... Sounds like that is what your therapist is thinking.

I'm not sure that there is depressive personality disorder as a dx in the current edition of the DSM... I know that it has been suggested for people who seem to be characterologically rather than situationally depressed, however.

Another alternative (that is in the current DSM) is dysthymia. It is described as being relatively 'low grade' depression, but it is worth bearing in mind that the 'low grade' is 'low grade' relative to severe Major Depressive Episodes where peoples functioning is severely impaired (and where medication may well be ineffective such that the person requires alternatives such as a course of ECT). From the first-person point of view people say that dysthymia isn't 'low grade' at all. That it feels horrible. It is persistent, however, rather than being situational, so it might be a better description of what is going on for you.

The only reason we say that depression is 'chemical' is because certain chemicals have been found to alleviate it. Similarly for schizophrenia and the like. As such, it would seem that your depression (since it is unresponsive to medication) would actually be LESS likely to be chemical than people who find that their depression is responsive to medications.

There are other options, however. One is structural damage (that can be reversed by way of life experiences). Another is content outside the designed range (or similar) where early childhood patterns of interaction with your attachment figures weren't able to provide you with the sense of vitality and acceptance that healthy individuals have. Either way... When the drugs don't work I guess that is the time to get serious about therapy...