The main reason I stay invisible is because there are certain days during which I just don't want people to know I'm around, whether it's because I don't feel like talking to people or for any other reason, and I just cba to click and reclick the button. So I stay invisible. I don't personally care if people see what I'm doing on the forum, I just have those days sometimes (fairly often, actually) when I want to remain hidden. If I don't want people to know I'm around, then I don't post or chat, I just lurk. I don't need to keep invisibility on, it's just too much of a hassle to go invisible when I want to.
It's the same reason I go invisible on Skype so often, there may be some people I want to chat with while there are others that I'd rather not even know I'm online.
If I'm gonna be honest, though, with so many people having Stalker Goggles nowadays, the invisibility feature is quite pointless. I wouldn't really care if it were removed.