Actually if the original one chakra is not properly flowing correct the clone will vanish. As seen when Sasuke stab his sword in Yamato to make him numb which disrupt his chakra flow and than the clone with Kabuto vanished so if Jiraiya Chakra flow is disrupted by Pain Sword his clone is gone.
Pain:
You must be registered for see links
Sasukes:
You must be registered for see links
PS I can't find the part where the clone disappear of Yamatos but in the Anime Of Rescue Sasuke Arc(not filler) his clone disappear.
THIS IS NOT CONFORM Just my thought