I don't know if anyone can prove that God determines the years, but, what we do know is that God, who exists outside of time, simply knows how long your days are. See, all the things that mark time like the rotation of the earth (1 day) or the orbit of the moon (1 month) or the orbit of earth around the sun (1 year) are things God created and He existed before that. He is the beginning and end and knew in the beginning what He will know in the end... so.... just as a lamb was slain before there was sin (Revelation 13:8) I think God simply knows when your last breath will be taken. Can He prolong that? Sure, we have an example of Him adding, what was it, 15 years to a life? But even then, I imagine, He knew before He created anything that He would do that, too.
Both predestination and free will exist in Scripture. And instead of choosing one of them over the other like so many do, we just need to wait on Him to show us how both can exist in Scripture. I think the answer rests in "which set of eyes are we looking through?" See, if we see through God's eyes, the eyes that can see the end from the beginning, we are predestined. But if we look through ours, and we don't even know if our next breath is our last... it is free will. I am saying that to say that if you determine to commit suicide, I imagine it will work and He will have known you would do that before He said, "Let there be" about anything.