I would have to disagree with you. Man cannot cure it, I think that’s true.
But Jesus raises people from the dead and he CURES mental disease including those who are bi-polar. I have see this myself.
The cure is his deep and unconditional love. More often than not, if you delve deep enough into a tortured soul, you’ll find CONDEMNATION. Doctors will tell you guilt and self-condemnation is what populates the mental wards. Jesus offers the gift of no condemnation and I have see it heal those that receive it mentally and emotionally.
GOD for His own reasons allows us to have afflictions which show His strengths through our weaknesses. Adversity being His tempering fire.
Mental health issues vary as to cause. Some can be traumatic events like PTSD or phobias. Some can derive from brain chemistry being deprived or saturated with too much or too little a chemical. It can come from neurotransmitter disorders. It can even come from a Urinary Tract Infection or Inner Ear Infection.
It's not the persons sins, lack of faith, or GOD is angry or displeased with the person etc. Bipolar can come from genetics and can be passed down, it can also come from substance abuse which is becoming more common.
Most mental illness except usually for the far more serious types are secondary {symptoms actually} of a primary physical disorder. You go tell a Shrink that Inner Ear Disorders can give you Anxiety and he will say you're nuts. You go tell an older General Practitioner the same thing and he'll likely say Yeap seen it a few times. And of course there is misdiagnoses all together.
Yes Jesus Christ can heal. However if healing is not granted the person afflicted should not be made to feel it was their fault a bearing guilt they should not be carrying. Remember Paul's affliction he prayed to be taken away? No one knows for certain what it was maybe partial blindness since many of his letters were written by persons he dictated them too. In that respect one passage does point to that as he talks about his own handwriting. Paul was an educated man.