abirdcall
(she/her)
There is no reason whatsoever to suspect that it would stop working after the first hit.
That's like saying there is no reason to suspect that drinking a potion of healing removes the contents of the potion after drinking it. A potion of healing doesn't say that it is one use only. It only says that using it requires an action.
It is a limitation on the duration that the poison will stay active on the weapon. It is not a magical reappearing poison which gushes forth as quickly as you can wipe it off. That is absurd.