Depending on circumstance, I can think of a few: work stress (many high-paying jobs are high-paying because they are highly demanding; the stress on the poor is perhaps shifted away from work and towards an inability to pay for things); social pressures (to maintain a high social standing, for example); and privacy invasions from the paparazzi. Certainly, not all rich people face these problems, but many of these would disproportionally affect the rich in my view.

I think relationships can he harder for rich people. Since you get to pick and choose all elements of your life, picking the people you spend time around is much more available to rich people.

And people are often after your money, which can really damage relationships between people.

You never know if someone likes you for you or your money.

Depression can ravage a person regardless of socioeconomic class. While wealthier people may afford better treatment, the affects are still there. Kate Spade is the most recent example that comes to mind.

There was research posted on hn which showed that poverty has a negative effect on cognitive functions

Being kidnapped for ransom?

Terminal cancer,etc.