I think the answer to this is 2-dimensional. Affluence could be a special problem if it is not properly managed. It is a problem when it is self-centred and designed mainly to cater for the needs of the owner alone without extending hands of fellowship to other member of the society both internally and externally. The questions of how it comes and many parts of it are vital in this case. On the other hand, affluence that is well-managed, environment-friendly, well-shared with others and used to cater not only for selfish interest but for the majority of people and for humanity sake will never be a special problem to the owner. 

It is not so much affluence that is the problem as inequality and also damaging forms of consumption. Wilkinson's book "The Spirit Level" is required reading on this subject. The UK and US would be classic examples of these phenomena with high levels of mental illness and inequality. Equally affluent (or even more so) countries like Denmark show less of these ill effects. I agree also with the previous answer.

The problem is, in my view, clearly the connection between affluence (and one could say also influence or political power) and economic and political inequality.   As Andrew McCulloch noted in his reply, this also gets to the issue of unequal consumption, which is a big and extremely important issue in the current global context of international (and national) economic inequality, and how forms of inequality and consumption interact to promote other inequalities and other detrimental outcomes such as ecological disorganization and destruction.  You can't really (in my opinion) talk about these issues without referring to Marx's analysis of capitalism and inequality, and modern theoretical and empirical studies relating that view to ecological destruction and disorganization (e.g., see for example, works by John Bellamy Foster [1992, The absolute and general law of environmental degradation under capitalism]; and numerous excellent empirical studies related to this approach by Andrew K. Jorgenson).  I would argue that the problem of inequality has never been "well-managed."  For example, examine the data from inequality.org (https://inequality.org/facts/global-inequality/)

In 2015, 0.7% of the world's population had a wealth share of one million dollars of more, and that 0.7% of the population owned 45.2% of global wealth. (And here, I am ignoring some refinements we could make here since as Oxfam reports, wealth is unevenly distributed among this group as well, with the EIGHT richest people in the world own $462 billion in wealth).

At the other end of the spectrum, 71% of the world's population owns less than $10,000 in wealth, and owns only 3% of global wealth.

Part of the issue with the above relates to the definition of "affluence," since being "affluent" in different national contexts can be defined relative to a nation rather than globally.  To get an idea of that issue in a national context we can refer to measures such as the GINI Index of income inequality.  (Although there are problems with the GINI index, ( see, http://www.hsrc.ac.za/en/review/hsrc-review-november-2014/limitations-of-gini-index)

Matthew Dada suggests that its not affluence, but how it is managed -- which might be correct -- and the question is -- what would a GINI index look like in a country where affluence was "managed properly"?   Denmark, for example, has -- compared to other countries -- a low GINI around 0.25.  Relative to other countries (e.g., US, 0.47) that is "good," but is 0.25 the best that can be achieved?  Is it appropriately defined as "well managed?"  So, it seems that there is some need to answer the question Dada raised about what "well managed" means before some conclusions can be reached.