This is the argument that Nagato intentionally wanted to get caught in Jiraiya's frog song. The credit goes to Blaze Release as he wrote it originally.
A stop in the flow of chakra whilst in genjutsu is usually enough to break you out from it but people are asking, rightly so, if thats the case then why didn't Nagato cut off his chakra while his three paths was caught. There is enough to suggest that Nagato purposely wanted to get caught.
Jiraiya
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is talking to Ma and Pa about how it is necessary to catch the three paths first rather than they first find Jiraiya and co. Jiraiya even admits that they would loose if the paths are aware of the incoming sound genjutsu. A few
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later, we find the three paths being aware that a genjutsu is being conducted and has established that its frogs singing, it is important to note that they haven't been caught and yet still make their way towards where the sound is coming from.
Once they enter the room we all know what happens as the three paths get caught in the
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after distractions and diversions done by Jiraiya. Note one of the paths say "You got me...." Now I believe thats said in a sarcastic tone hence why there are so many dots followed by but its up to your own interpretation. Jiraiya then goes on to
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how it is important not to underestimate your opponent.
After Jiraiya "kills" the three paths he strongly believes that its finally
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. However we know that is not the case as
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says something ironic to Jiraiya and the rest is history.
Nagato could've stopped sending chakra to the chakra rods anytime but didn't. Call it plot no jutsu or clever play by Nagato. I firmly believe its the latter.