This question speaks to me. My answer is Yes, but not so much when I am able to simply observe as opposed to react.
Do not focus on the philosophy of why it is that you feel that way. It's true that many of us who have suffered hardships for a good part of our life have a predisposition to "happiness". But whilst such statements have elements of truth in them; they come across more as prescription based reasoning that obscures a persons unique perspective. Unfortunately such an outlook can have negative connotations, despite the well meaning in which it's often given.
For me, it's best said - "It's not a sufferer's inability for happiness that makes them sad, but more the reliance that others place on happiness itself."
That outlook for me, brings more truth than another's well meaning prescription based reasoning. It's the other side of the coin from which understanding can only come from ones own perspective, not someone else's. I have a few prescriptions of my own, like - "sliver spooned upbringing ..." No matter how much I unwittingly use such prescriptions, those who'm I claim to have such a spoon in their mouths, will always claim not to see them.
____________________________________________
I feel I understand your question well and thank you for it. My perspective tells me that that the trigger is more key than the "happiness" itself. Define the trigger rather than that which seems you are missing. That which seems more appealing and plays on loss. That which seemingly beckons a sense of guilt for having suffered at all.
That last sentence is hard for me to explain, but a key of which I am trying to speak/seek and or be. Embrace this reaction that we term as sadness and see it as something else. Perhaps an opportunity which brings a sense of clarity which can only ever come, from your own experiences. In this regard - sadness need not be suffering at all.
( I am beginning to see how suffering is a western term - it's helping to drop the notion all together and see it in another light - or no light at all)
__________
I hope some of that helps. I really appreciate this question. I feel that too much shedding of light has the opposite effect of illuminating, especially for those of us who are said to be observing from the shadows.
On a hot day - such a perspective brings relief.