We know that the Helcaraxë formed a bridge between Aman and Middle-earth during the First Age, but its fate in later ages remains mysterious. In the destruction of the War of Wrath at the end of the First Age, Beleriand (at the eastern end of the Grinding Ice) sank beneath the Sea, so at least some of the Helcaraxë must presumably have been lost at that time.
In the late Second Age, at the time of the Downfall of Númenor, the entirety of Aman was taken out of the world of Men, irrevocably dividing Middle-earth from the Blessed Realm. That presumably included any remaining physical link across the Helcaraxë, so if any of the western part of the Ice survived the First Age, it would certainly no longer have been accessible after II 3319, the year of the Downfall.
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