Aragorn could heal Éowyn with Athelas, but he could not heal Frodo of a similar wound. Why not? Both wounds resulted from a Black Rider.
But Eowyn was not pierced by the sword of the Nazgul (specifically the Witch-King of Angmar, the most powerful of the Nine) with a piece of the blade working towards her heart, about to make her a wraith!
Though Frodo and Eowyn faced the same opponent, Eowyn's only injury was from a blow to her shield-arm and the Black Breath, which Aragorn found fairly easy to treat in most Men with athelas. Frodo, on the other hand, was pierced directly by the Nazgul's blade, and the piece of the blade which was left in his body was unable to be removed by Aragorn.
The injuries done by the Witch-King were therefore completely different in scope between Frodo and Eowyn. Because Aragorn could not remove the shard of the Nazgul's blade from Frodo's body, his injury would have certainly caused his death if not for the healing skills of Elrond. Eowyn's injury boiled down to a broken arm and the Black Breath, which Aragorn normally found easy to heal, except that Eowyn resisted healing since she had lost her will to live.
They were different wounds. Frodo had been stabbed by a Morgul Blade, a splinter had broken off and was making it's way to his heart. Eowyn's wound was nothing like this - her arm was broken by a mace and she was suffering from a dose of Black Breath. So you're very wrong to say "he could not heal Frodo of a similar wound" because it wasn't even a similar wound to begin with.
"Both wounds resulted from a Black Rider" is a very limited way of looking at it. It's quite clear in the books that the chief problem with Frodo's wound was the Morgul Blade splinter, and so Aragorn could not heal it.