Firstly, consider the form of the rosary. It is 10 repetitions of the 'Hail Mary' for five times. What did our Lord say about repetitious prayer? "When you pray, go into your room, and when you have shut your door, pray to your Father who is in the secret place; and your Father who sees in secret will reward you openly. And when you pray, do not use vain repetitions as the heathen do. For they think that they will be heard for their many words" (Matthew 6:6,7). Prayer is the spontaneous expression of the heart before God - of praise and thanksgiving, confession and petition. Repeating the same prayer over and over again tends to dull the mind. Such repetitions are vain and pagan.
Secondly, and more importantly, note that Jesus told us to address our prayer to God. "Pray to your Father." There is no example or permission in the whole Bible of Christians praying to anyone except God. And for a good reason. God is able to hear our prayers from heaven (there must be thousands of people praying at this very moment), because He knows all things. "whatever prayer, whatever supplication is made by anyone...then hear in heaven Your dwelling place, and forgive, and act, and give to everyone according to all his ways, whose heart You know - for You alone know the hearts of all the sons of men" (1 Kings 8:38,39). God knows our heart and He hears our prayer. But Mary is not God. She is a finite human being. She does not know the hearts of all people. God alone knows them. "For You ALONE know the hearts of all the sons of men."
Thirdly, when Catholics pray to Mary: "Pray for us sinners, now and in the hour of our death," they are placing their trust for salvation in the hands of a creature, rather in the Lord and Savior, Jesus Christ. Mary herself did not do so because she acknowledged God as her Savior (Luke 1:47). The Catholic Catechism explains the significance of the 'Hail Mary': 'Our trust broadens further, already at the present moment, to surrender the hour of our death wholly to her care' (paragraph 2677). Please find Act 7:59 in your Bible and read about a Christian at the very moment before his death. To whose care did he commit his spirit before he died? And then ask yourself, to whom am I surrendering the hour of my death - to Mary (a saved creature) or to the Lord Jesus (our God and Savior)?