In High income improves evaluation of life but not emotional well-being, the authors make the distinction between two factors aspects to happiness and then evaluate each aspect's relation with income.
The first one is emotional well-being, which they define as:
Emotional well-being (sometimes called hedonic well-being or experienced happiness) refers to the emotional quality of an individual’s everyday experience—the frequency and intensity of experiences of joy, fascination, anxiety, sadness, anger, and affection
that make one’s life pleasant or unpleasant.
The second is life evaluation:
Life evaluation refers to a person’s thoughts about his or her life.
Additionally, they also measured what they called "blue effect," which the "average of worry and sadness," and "positive effect," which is defined "by the average of three dichotomous items (reports of happiness, enjoyment, and frequent smiling and laughter)."
After evaluating the results of the 2008 and 2009 Gallup-Healthways Well-Being Index, the authors found that emotional well-being correlates with income, up to an an annual income of $75,000, after which point it has. They also found that both positive effect and blue effect correlates with income (positive effect positively and blue effects negatively), also only up to a certain point. On the other hand,m life evaluation correlated strongly with education and income.
In light of those results, they conclude that (emphasis mine):
The data for positive and blue affect provide an unexpectedly sharp answer to our original question. More money does not necessarily buy more happiness, but less money is associated with emotional pain. Perhaps $75,000 is a threshold beyond which further increases in income no longer improve individuals’ ability to do what matters most to their emotional well-being, such as spending time with people they like, avoiding pain and disease, and enjoying leisure.
Considering that wealth reduces sadness and worry, it's unlikely that an increase in wealth would result is a loss of happiness, unless wealth comes with an associated cost (sickness, for example). Wealth alone, however, does not seem to cause unhappiness.
If you require a more global look at the problem, there is Wealth and happiness across the world: material prosperity predicts life evaluation, whereas psychosocial prosperity predicts positive feeling., a review of the Gallup World Poll, which "was used to explore the reasons why happiness is associated with higher income."
It finds that income only has a minor impact on emotional well-being, and that it is psychological needs that affects one's emotional well-being (emphasis mine, again):
Income was a moderately strong predictor of life evaluation but a much weaker predictor of positive and negative feelings. Possessing luxury conveniences and satisfaction with standard of living were also strong predictors of life evaluation. Although the meeting of basic and psychological needs mediated the effects of income on life evaluation to some degree, the strongest mediation was provided by standard of living and ownership of conveniences. In contrast, feelings were most associated with the fulfillment of psychological needs: learning, autonomy, using one's skills, respect, and the ability to count on others in an emergency. Thus, two separate types of prosperity - economic and social psychological - best predict different types of well-being.
In any case, neither studies found a negative correlation between wealth and happiness.