The present tense implies that this demonstrating is an ongoing act that keeps happening today. And will keep happening tomorrow.
The past tense “died” implies that the death of Christ happened once for all and will not be repeated. “Christ also suffered once for sins, the righteous for the unrighteous, that he might bring us to God” (1 Peter 3:18).
Why did Paul use the present tense (“God demonstrates”)? I would have expected Paul to say, “God demonstrated (past tense) his own love toward us, in that while we were yet sinners, Christ died for us.” Was not the death of Christ, when it happened, the demonstration of God’s love? And did not that demonstration happen in the past?
I think the clue is given a few verses earlier. Paul has just said that “suffering produces endurance, and endurance produces character, and character produces hope, and hope does not put us to shame” (Romans 5:3–5).
In other words, the goal of everything God takes us through is hope. He wants us to feel unwaveringly hopeful through all tribulations.
But how can we?
Paul answers in the next line: “Because God’s love has been poured into our hearts through the Holy Spirit who has been given to us” (Romans 5:5). God’s love has been poured into our hearts. The tense of this verb means that God’s love was poured out in our hearts in the past (at our conversion) and is still present and active.
God did demonstrate his love for us in giving his own Son to die once for all in the past for our sins (Romans 5:8). But he also knows that this past love must be experienced as a present reality (today and tomorrow) if we are to have patience and character and hope.
Therefore, he not only demonstrated it on Calvary; he goes on demonstrating it now by the Spirit in our hearts. He does this by opening the eyes of our hearts to taste and see the glory of the cross and the guarantee it gives that nothing can separate us from the love of God in Christ Jesus (Romans 8:38–39).