I'm not sure if anarchists are more prone to depression or not, I don't have the statistics nor an equal enough perspective to compare the depression in anarchist and non anarchist circles.
However, many anarchists do view the world in a way that I think can lead to burn out, depression, and hopelessness. Anarchists have a discontent with the world, and feel that our understanding of the world clearly answers, or at least addresses, all the world's problems, and as such we ought to do something about all of these things. This can be an amazing struggle that empowers one to lead a life of conflict that works toward improving their life and maybe those around them or it can be a huge burden that looks like defeat every step of the way.
Its important to address what we, as individuals, want out of the world, not just what we want to change about it, and do it. If you want your ideas to be heard, write a zine, make propaganda, do banner drops, organize a bookfair (conversely, if you feel getting ideas out there is more effort than reward, don't); if getting out anger feels good, go break something or yell at a cop (conversely if it causes stress and anxiety or feels useless, don't feel obligated to be a smashy-smashy anarchist); if gardening and seed saving are important ways of reconnected and saying 'fuck you' to Monsanto, start a guerilla gardening project or something, etc etc etc etc etc. Find what makes you feel good about conflict and don't worry about winning, search for value in what you get out of it. And remember that it is not anyone's job to save the world, or even to 'save' anyone but themselves. I think there needs to be a little more self care on an individual level in this scene. Maybe I sound like a 'lifestylist', but what good is a analysis of the problems we face, if we aren't using it to find happiness and fulfilment in our own life.