Tolkien obviously drew heavily on Beowulf for "The Hobbit" -- I mean, Smaug basically is Beowulf's dragon. He flies, he breathes fire, he hoards treasure, he is roused to fury by the theft of a cup from that hoard, and he is slain by piercing his vulnerable belly, by a foe whose home he had incinerated.
So, where can we find a weapon described as having "never failed" in Beowulf?
Its steel edge, hard with bloodshed,
gleamed with a design: poison
twigs entwined. It failed no man
in battle or adventure
or wherever armies gathered.
Why, it's... Hrunting. The sword that accomplishes exactly nothing against Grendel's mother.
Then let's turn to the battle with the dragon. Beowulf brings in another ancient sword with a heroic name, Naegling. It likewise accomplishes more or less nothing, shattering against the dragon's armor. Then Wiglaf steps up and stabs the dragon's belly with a sword which is described merely as "old," and Beowulf finishes off the monster with the knife in his byrnie, which as far as we can tell is just a plain old dagger Beowulf was carrying.
Given that -- as I said -- Smaug is the Beowulf dragon with serial numbers filed off, and given that the vulnerable spot on his belly receives vastly more attention than the arrow which pierces that spot, it's a huge reach to claim that a magic weapon was required to kill Smaug, or that a weapon described with a storied history is necessarily a magical one.