They often don't care about themselves enough to get good help or don't have the energy to do so.
Absolutely Dubstepped people with mental illness often " fall through the cracks" if they don't have anyone who is willing to seek help for them. Either because they don't approve of the help offered, like JWs, are being shunned or they just don't pick up on the cues.
Remember most depressed people don't see a lot of people and withdraw into themselves. This alone puts JWs at risk since if you fail to get involved in JW life you will be pre-emptively shunned too, making them even more alone.