God's work does not happen over a day or a week. He works in our lives over a lifetime. Unfortunately, according to the Parable of the Soils in Matthew 13, many will fall away too early and not bring forth fruit to perfection. Only the fourth soil does that, and it requires patience.
Trials and troubles are part of the package God uses to perfect us, and we need patience to learn the lessons God is teaching us in trials. The general overview of this process is given in Romans 5:3-5, "Not only that, but we rejoice in our sufferings, knowing that suffering produces endurance [or patience], and endurance produces character, and character produces hope, and hope does not put us to shame, because God’s love has been poured into our hearts through the Holy Spirit who has been given to us."
In the end, the "perfect work" is hope. After we undergo our trials again and again, and find God being there with us no matter what and still working in our lives, we have an expectation (hope), that all will be well, no matter the trial, and so we are more patient when the next trial comes along.