Very common. Especially in such a turbulent place as the Austria-Hungarian Empire, where Franz Joseph was from.

The Russian Empire for example witnessed the violent killings of 5 of its Tsars (Kings) in a relatively short period of time. Two of them, Tsar Alexander II and Tsar Nicholas II we’re grandfather and grandson.

Suicides were also very common, as you pointed out in your question. Many members of royal families across Europe often engaged in very scandalous activities, particularly sex, which was seen as reprehensible at the time. If information about these activities got out, as it often did, the person would be so embarrassed that they would kill themselves.

In short, being a royal was certainly not always a good thing.