Hey man. Funnily enough, I was in same exact situation until last Valentine's day. Lasted for roughly 3 months.
Anyway, I may not know the extent and details of your situation, but I imagine you've gotten the same drivel like myself, ranging from "I can't be an adequate girlfriend for you right now" to "I don't feel comfortable being a burden upon others and especially you." etc, etc.
My sincere advice is to discern thoroughly whether her depression is merely a cover for an underlying problem, or an actual issue she is going through.
In my case, even though she'd message/call every single day of relationship, several weeks into the relationship, she grew increasingly distant to the point where we'd see one another like two times per week most. Of course, it wasn't a question of unavailability, because she'd still hang out with her friends, because in accordance to her, to them, she can pretend that she's not alright, and doesn't have an obligation/stress of being a girlfriend.
I found and it turns out she's been still keeping contact with an ex of 4 years, and has been seeing him without even saying a word about it.
Now mind you, this girl does have actual depression. She has extended periods of sleep deprivation, suicidal thoughts, abrupt loss of appetite etc, all the nasty stuff accompanying the illness. But ultimately, my point is not to allow or let depression to be used as a convenient tool to mask underlying issues.
It is also not my aim to hammer insecurity into you, but these people easily grow into the roles of pathological liars, because donning masks in everyday environment is such a commonality for them, that it becomes their instinct to pretend and deceive, even though doing harm may not be their actual, moral intent.