Age is a risk factor for depression when we look at the entire lifespan. Does that hold true in a population of >60 years old?
In addition to the articles that @Seanny provided in the comments, I think this study addresses your question pretty well. A couple of idiosyncrasies about the sample: from rural Germany, primary care attenders, 75 and over (Weyerer et al., 2008).
Results are somewhat mixed: univariate analysis shows a positive relationship between age and depression (accounting for sex), while adjusting for all possible confounding variables make the effect not statistically significant (though still positive).
What does this mean? Yes, there is a positive relationship between age and depression. However, the relationship may not be distinct from other aspects of old age (mobility impairment, visual impairment, etc.) that increase in prevalence as age increases.
Weyerer, S., Eifflaender-Gorfer, S., Köhler, L., Jessen, F., Maier, W., Fuchs, A., … Bickel, H. (2008). Prevalence and risk factors for depression in non-demented primary care attenders aged 75 years and older. Journal of Affective Disorders, 111(2–3), 153–163. http://doi.org/10.1016/j.jad.2008.02.008