"Good" people, believers DO end their own lives at times. BUT it isn't because God failed. There are a myriad of reasons why a believer could complete such an act, maybe something as "simple" as the person God sent to help them refused to go... or the negative thinking the person had was never countered but minimized... ultimately they gave up on this life.
Paul had such thoughts, but God brought him through it. My ideas would also follow this line that "wow, why continue to battle this horrible life I have when I can go home to God and live in peace?" And indeed, sometimes life is very, very difficult for long periods of times (I am in my 30th year of disabling pain and injury). BUT HE GIVETH MORE GRACE.
Paul stated it would be easier to go home to Christ, but that he stayed because it benefitted those still living. And indeed his life did--and still does! We don't know just what is around the corner for us, and it could be that God has great things in store. The devil doesn't know what God has for us, he just attacks and attacks trying to keep us from HIS will.
Realize the battle is not yours...this depression...but of the devil (I don't know anyone who purposely sits down in their life and says they're going to become depressed and hate their life!) GOD will fight this fight for those who are depressed... lean on Him, in His care, under His wing, rest upon His bosom... be still and KNOW that HE IS GOD and loves you and will bring you through.