Suicides prevail at both ends of the spectrum of social interaction: too much or too little [1]. It's not just at the too little end. Examples of too much social interaction leading to suicides: prison suicides, overworked stressed out students, suicides due to too much debt or career failure, individuals, usually women, left alone to take care of too many children alone without support, and altruistic suicides such as when elderly go into the wilderness to free up resources, or soldiers jumping on grenades. It's not just loneliness that kills. You have to plan ahead and manage your interaction such that you don't leave yourself without anyone, and have a support network and realistic expectations in life.

[1] http://en.wikipedia.org/wiki/Suicide_(book)#Types_of_suicide