This is a Pathfinder 2 question.
The rules for poisoning weapons seem contradictory, or at least redundant. Two different sections deal with this; I'm going to cite them both because I'm thinking about running a Rogue/Alchemist and so they are both relevant.
PH pg. 550, the relevant bit under "Method of Exposure" reads (as amended):
Injury: An injury poison is activated by applying it to a weapon or ammunition, and it affects the target of the first Strike made using the poisoned item. If that Strike is a success and deals piercing or slashing damage, the target must attempt a saving throw against the poison. On a failed Strike, the target is unaffected, but the poison remains on the weapon and you can try again. On a critical failure, or if the Strike fails to deal slashing or piercing damage for some other reason, the poison is spent but the target is unaffected.
Note that it first says that being poisoned affects "the first Strike made", but then goes on to tell us the consequences of missing and critically failing with that Strike. If being poisoned only affects the first Strike you make, the rest of the text is unnecessary.
Similar on PH pg. 185, in the description of the Rogue's Poison Weapon feat (again as amended by errata):
You apply a poison to the required weapon; if you're not holding a poison and have a free hand, you can Interact to draw a poison as part of this action. If your next attack with that weapon before the end of your next turn hits and deals damage, it applies the effects of the poison, provided that poison can be delivered by contact or injury. If you critically fail the attack roll, the poison is wasted as normal.
Again, it tells us that the poison only has an effect if the "next attack with that weapon [...] hits and deals damage" -- and then goes on to remind us what happens on a critical failure even though that can never be relevant with the rules written as they are.
So that gives us two possible interpretations: Either a weapon stays poisoned until you critically fail your attack or hit without dealing damage, or it stays poisoned until you next attack with it and then stops being poisoned no matter what the outcome was. As the person playing the Rogue/Alchemist, I of course want the former to be correct -- it's likely to make a very big difference! The rules as written suggest that they went back and forth on this and then emitted a confusing set of rules.
Which way should this be played and why?