The Hyundai driver began the second running of Aghii Theodori just 1.3sec behind nine-time world champion Sébastien Ogier, having yielded the lead to the Frenchman on Sunday's opening stage. The pair posted identical times for SS15, Loutraki 1, but any hopes of that battle continuing were dashed on SS16 when Neuville suffered damage to both rear tyres.
With 10km remaining, he and co-driver Martijn Wydaeghe lost almost one minute to Ogier and now trail the Frenchman by 54.8sec heading into the Wolf Power Stage.
"We were very unlucky," Neuville said. "I don't know what happened. I got a low pressure alarm first on the left, and then it stabilised, and then suddenly we got a rear right, and at the end, two rear punctures to finish the stage. So what can you say? It would have been nice to fight until the end against Sébastien, but that's it. Honestly, we're all disappointed now, and the team would have deserved that victory here. We were on pace, but... that's how it goes."