Perhaps there's some unusual trigger that allows him to continue using it based on how many weapon skills he "Dodges" (kind of like powered up Yaegesumi from Tenzen II).
I'd appreciate if another ranged job could try to corroborate my results below. COR, RNG or any job with decent ranged attack can do it.
Hypothesis: Qiqirns track weapon skills. Each weapon skill used against Qiqirn that doesn't open or close a skillchain adds to an invisible counter (time based or stacking effect). When the counter reaches a certain threshold, Qiqirn uses SP.
Methodology: Ambuscade v1 E. COR/DNC with main sword, offhand dagger, and gun. PLD/WAR to hold Pilferer (boss). Qiqirn Mine ignored and allowed to detonate. 2 RDM and 2 WHM Trusts fill the remaining slots.
COR stores TP on Scoundrel (add) with melee attacks. Use simple, low-damage melee WS spaced apart and guaranteed not to chain (Burning Blade, Shining Blade, Flat Blade). If Perfect Dodge occurs, switch to ranged attacks for TP gain and then deliberately miss with melee WS against target while PD is active. Repeat until you die from a Steal HP-Kibosh one-two punch.
Results: Scoundrel reliably uses Perfect Dodge within 5 WS that do not chain. Furthermore, by gaining TP with ranged attacks during Perfect Dodge, you can reliably induce Scoundrel to use Perfect Dodge several times in a row.
Conclusion: The secret to this month's Ambuscade was never a question of how many skillchains you do, but how many you fail to do. This appears consistent with all of the findings in the thread so far: coordinated SCs thwart PD, high-damage SCs still face PD, back-to-back PDs when people whiff weapon skills that are guaranteed not to chain.
I assume boss follows the same logic, but he pulls from one of four SPs (PD, MS, HF, BW).