The phrase “midst of my days” means middle of my life. The writer is thinking, “I am not old and therefore I am not ready to die.” The psalmist is in effect begging for God for more years to live
He does not know as no one knows how much time one has in life. There is no guarantee of how long one will live their life. One has to learn that living to make a difference for God is the greatest purpose one can have in life and that time should begin now if it hasn't already.
Although this practically may look different for every believer, giving one’s life to God is about our attitude. If there is some specific task He wants us to do, we need to ask Him. I have learned God is more than willing to guide us down the path He desires for our lives if we let Him. I then find that by watching my life and going in the direction that I believe God is leading me, it becomes obvious over time just how He is leading our lives. It all begins by asking God to help us and lead us down the path He desires for our lives. I also find that if God wants us out of our particular situation, He will make it happen if we are willing to try to change that situation.
God’s timing is always perfect and no matter how young or how old we are, the God we trust in is willing to guide our lives if we let Him. He is well aware of how old we are and what we desire to accomplish in our lives. The secret is to remember that our lives belong to Him in the first place. We can’t change our past, but we can live to make a difference for Him today and tomorrow. How we actually make that difference is up to Him to lead us, which He is more than willing to do if we trust Him.