My friend speaks often about her Depression and I'm going to tell her to stop.
Is this something she brings up regularly?
Yes, and it's usually when she's drunk. It's pathetic.
While her speaking of her Depression might be tiresome at times you shouldn't tell her to stop talking about it. Doing so might make her shut down and worsen her Depression.
Nah, I don't think I would make it any worse if I tell her to stop mentioning it.
Your friend's feelings are valid and they're probably talking of them because they're in need of support. Telling your friend to stop expressing themselves could make them feel hurt and rejected. Try to be more understanding and compassionate to their current suffering and struggles.