Psalm 73:26 - My flesh and my heart fail; but God is the strength of my heart and my portion forever.
This is a good verse to remember and pray for all kinds of weakness and not working well of the flesh and heart - it puts its failures in perspective. The weakness and unreliableness of the flesh is expected; only Christ is the Rock. (2 Corinthians 1:9, 2 Corinthians 4:7, 2 Corinthians 5:1, 2 Corinthians 12:9).
This verse and even more explicitly Romans 8 and 1 Peter 5:10 also show that whatever suffering we deal with, if we have new life in Christ, the suffering is temporary and the life we already have in Christ is eternal.
I listen to a lot of messages from John Piper - I was trying to think of one that might be helpful and I thought of one that I heard recently on Psalm 42. It deals with how a Christian hopes in God through difficulty. There is video and audio here -
Spiritual Depression in the Psalms