Joseph, L. J., & Black, P. (2012). Who's the man? fragile masculinities, consumer masculinities, and the profiles of sex work clients. Men and Masculinities, 15(5), 486-506.
Huysamen, M., & Boonzaier, F. (2015). Men’s constructions of masculinity and male sexuality through talk of buying sex. Culture, Health & Sexuality, 17(5), 541-554.
Kong, T. S. K. (2015). Romancing the boundary: Client masculinities in the chinese sex industry. Culture, Health & Sexuality, 17(7), 810-824.
Wepener, I., Learmonth, D., McLeod, K. L., & Chikte, Z. (2013). Beyond the tease: Exploring men's constructions of paying for sex in South Africa. Psychology Research, 3(12), 749.
One thesis...
Jones, Z. K. (2013). "Emotional landscapes" and the value of sex: Exploring the lived experiences of sex workers' clients (Order No. MR95470). Available from ProQuest Dissertations & Theses A&I: Social Sciences; ProQuest Dissertations & Theses Global: Social Sciences. (1469873536).
Some nice references there from Adelheid. Jo Brewis and I touched on this in our book Sex, Work and Sex Work (Routledge 2000) and we did find from interviews with sex workers in the highly stratified market of NSW that there was a significant demand for this kind of service, and that this increased at the top end of the market. We didn't do any client interviews though. If you are also interested in men using male sex workers for similar purposes, this empirical study by Sue Joseph is now 20 years old but uncovered a surprisingly extensive practice, and definitely spoke to male isolation and loneliness:
Luise White, 1990, The Conforts of Home: Prostitution in Colonial Nairobi. Prostitutes of Nairobi, Kenya, in early 20th century, specialized in a range of services including washing clothes of clientes, feeding them, and giving them emotional care. Many of their clientes were European colonials.
I understand that my answer comes late, but if you're still researching this, I strongly recommend your read Elizabeth Bernstein's book Temporarily Yours: Intimacy, Authenticity, and the Commerce of Sex. Particularly, in Chapter 5, she discusses the rise of the phenomenon of the "girlfriend experience" within sex work. He study includes quotes from clients about how they look for intimacy with sex workers.
Loneliness, and shame about one's body will enter the many reasons why men will contact a sex worker. It can be about sex, and it can be about wanting to be touched. It can be because he does not want a divorce, but for whatever reason the sexual part of the marriage is causing hurt and frustration.
It can be because he is ashamed of his desires but she will not make him feel that shame.
As researchers if we want to make sense of why men pay for sexual services we must first respect their decisions and pay attention to what they tell us.