Any blessed item retains its blessing until it is either relegated to secular use or destroyed. So no, it is not the blessing that is lost over the course of one year but rather, the verdancy of the palm fronds; the once supple, green leaves in a year’s time turn faded and dry out.
This traditional practice of burning ashes is filled with all sorts of symbolism. Most notably, we seen in the burning of old, dried palms the frailty of our human selves and the guilt of our shortcomings in failing to love and serve the Lord in our lives as we should have–the way we did when we heralded His triumphant coming with those very same fronds on the previous year’s Passion Sunday. In hopefulness, however, we look forward to the upcoming Passion Sunday and our Heavenly birth in the Resurrection on the week that follows, Easter!
I hope that helps clear it up for you.