Personally, I'm likely to houserule Razor-Edged to say that when it inflicts no damage, its Deadliness is reduced by (some number, probably 2-3) and it loses the ability to spend Opportunities for additional Deadliness, and it can be restored when resharpened by a competent swordsmith during downtime.
I recognize that there's realism to the current rule, but generally I'd rather favor Rule of Cool over gritty realism in my games, especially with regards to an iconic weapon of the genre. This way, there's still some downside to whacking something tough with your carefully refined ancestral weapon, but it shouldn't make players afraid to use the most commonly-depicted weapon in the setting.