Hello,

statistically speaking the poison procs every five hits. Based on assassins high atk speed and the possibility to animation-cancel auto-attacks with weaving (approx. doubling the hit count per second) it is almost impossible for the poison to run out as long as the assassin is attacking.
One could check the proc rate while using a bow to hit some dummies. In my quick test the poison procced every 4-6 auto-attacks in average, so I don't see any issue here.

Greetings,
Estrayl